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   "execution_count": 1,
   "metadata": {
    "tags": [
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   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *          "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
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   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Bias and Variance\n",
    "\n",
    "In this section, we provide a different way to think about the problem of over- and underfitting. We carry out a simulation study where we generate synthetic data from a model of our design. This way, we know the true model, and we can see how close we get to the truth when we fit models to the data. \n",
    "\n",
    "We concoct a general model of data as follows:\n",
    "\n",
    "$$ y = g(\\mathbf{x}) + {\\epsilon}$$\n",
    "\n",
    "This expression makes it easy to see the two components of the model: the signal $g(x)$ and the noise $ \\epsilon $. In our model, we assume the noise has no trend or pattern; constant variance; and each observation's noise is independent of the others'. \n",
    "\n",
    "As an example, let's take $ g(x) = \\sin(x) + 0.3x $ and the noise from a normal curve with center 0 and SD = 0.2.  We can generate data from this model with the following functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return np.sin(x) + 0.3 * x\n",
    "\n",
    "def gen_noise(n):\n",
    "    return np.random.normal(scale=0.2, size=n)\n",
    "\n",
    "def draw(n):\n",
    "    points = np.random.choice(np.arange(0, 10, 0.05), size=n)\n",
    "    return points, g(points) + gen_noise(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate 50 data points $ (x_i, y_i)$, $i=1, \\ldots, 50 $, from this model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "xs, ys = draw(50)\n",
    "noise = ys - g(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot our data, and since we know the true signal, we can find the errors and plot them too:"
   ]
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_full = np.linspace(0, 10, num=100)\n",
    "y_true = g(x_full)\n",
    "pewter = \"rgba(153, 157, 160, 1)\"\n",
    "charcoal = \"rgba(34, 32, 33, 1)\"\n",
    "\n",
    "fig = make_subplots(rows=1, cols=2)\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=xs, y=ys, mode=\"markers\", line_color=pewter), row=1, col=1\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=y_true, line_dash=\"dash\", line_color=charcoal),\n",
    "    row=1,\n",
    "    col=1,\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=xs, y=noise, mode=\"markers\", line_color=pewter), row=1, col=2\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=[0, 10], y=[0, 0], mode=\"lines\", line_color=charcoal),\n",
    "    row=1,\n",
    "    col=2,\n",
    ")\n",
    "\n",
    "fig.add_annotation(x=1, y=0.45, text=\"Noise\", showarrow=False, row=1, col=2)\n",
    "\n",
    "fig.update_yaxes(range=[-0.6, 0.6], row=1, col=2)\n",
    "fig.update_layout(height=250, width=450, showlegend=False)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot on the left shows $g$ as a dashed curve. We can also see that the $ (x, y) $ pairs form a scatter of dots about this curve. The righthand plot shows the errors, $ y - g(x) $, for the 50 points. Notice that they do not form a pattern.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we fit a model to the data, we minimize the mean square error. Let's write this minimization in  generality:\n",
    "\n",
    "$$\n",
    "\\min_{f \\in \\cal{F}} \\frac{1}{n} \\sum_{i = 1}^{n} [y_i - f(\\mathbf{x}_i)]^2 \n",
    "$$\n",
    "\n",
    "The minimization is over the collection of functions $ \\cal{F} $. We have seen in this chapter that this collection of functions might be polynomials of 12 degrees, or simply bent lines. An important point is that the true model, $g$, doesn't have to be one of the functions in the collection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take $ \\cal{F} $ to be the collection of second-degree polynomials; in other words, functions that can be expressed as $ \\theta_0 + \\theta_1 x + \\theta_2 x^2$. Since $ g(x) = \\sin(x) + 0.3x $, it doesn't belong to the collection of functions that we are optimizing over.\n",
    "\n",
    "Let's fit a polynomial to our 50 data points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=2, include_bias=False)\n",
    "poly_features = poly.fit_transform(xs.reshape(-1, 1))\n",
    "\n",
    "model_deg2 = LinearRegression().fit(poly_features, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitted Model: 0.98 + -0.19x + 0.05x^2\n"
     ]
    }
   ],
   "source": [
    "print(f\"Fitted Model: {model_deg2.intercept_:.2f}\",\n",
    "      f\"+ {model_deg2.coef_[0]:.2f}x + {model_deg2.coef_[1]:.2f}x^2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we know the true model is not quadratic (because we built it). Let's plot the data and the fitted curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
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   "source": [
    "poly_features_x_full = poly.fit_transform(x_full.reshape(-1, 1))\n",
    "ys_fit_full = model_deg2.predict(poly_features_x_full).flatten()\n",
    "\n",
    "fig = make_subplots(rows=1, cols=2)\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=ys_fit_full, line_color=charcoal), row=1, col=1\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=xs, y=ys, mode=\"markers\", line_color=pewter), row=1, col=1\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=ys_fit_full, line_color=charcoal), row=1, col=2\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=y_true, line_dash=\"dash\", line_color=charcoal),\n",
    "    row=1,\n",
    "    col=2,\n",
    ")\n",
    "\n",
    "\n",
    "fig.update_layout(height=250, width=500, showlegend=False)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quadratic doesn't fit the data well, and it doesn't represent the underlying curve well either because the set of models that we are choosing from (second-order polynomials) can't capture the curvature in $ g $. \n",
    "\n",
    "If we repeat this process and generate another 50 points from the true  model and fit a second-degree polynomial to these data, then the fitted coefficients of the quadratic will change because it depends on the new set of data. We can repeat this process many times, and average the fitted curves. This average curve will resemble the typical best fit of a second-degree polynomial to 50 points from our true model. To demonstrate this notion, let's generate 25 sets of 50 data points and fit a quadratic to each dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(n):\n",
    "    xs_new = np.random.choice(np.arange(0, 10, 0.05), size=n)\n",
    "    ys_new = g(xs_new) + gen_noise(n)\n",
    "    X_new = xs_new.reshape(-1, 1)\n",
    "    mod_new = LinearRegression().fit(poly.fit_transform(X_new), ys_new)\n",
    "    return mod_new.predict(poly_features_x_full).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "fits = [fit(50) for j in range(25)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can show on a plot all 25 fitted models along with the true function, $g$, and the average of the fitted curves, $ \\bar{f} $. To do this, we use transparency for the 25 fitted models to distinguish overlapping curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
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            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "baxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "bgcolor": "white",
           "caxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           }
          },
          "title": {
           "x": 0.5,
           "xanchor": "center"
          },
          "width": 350,
          "xaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          }
         }
        },
        "width": 400,
        "xaxis": {
         "autorange": true,
         "range": [
          0,
          10
         ],
         "type": "linear"
        },
        "yaxis": {
         "autorange": true,
         "range": [
          -0.27730897548912914,
          5.268870534293453
         ],
         "type": "linear"
        }
       }
      },
      "image/png": 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6z25WXVOjotSsnOwsyZw2E3pgYECjk/uHhyUyIkI2HLLe63tbpNBrE9oGBoXufgcMCt3tX4sUut+/boXC9vZ2nYpy3HHHrYgT+/v7ZdeevQqEWZmZkp2V6ZNzsB/NKtQo0sFcVFggSYkHNqzQ0FJZVa33Rv+QlLKNufOJ+W0Tby1gUOitBf378waF/u0fX5zOIoW+sKL/7uFWKLzvvvt0rjEj8ZZ7EaUDCOmiJjpIlNAXSzUI95YLwBkSHCwlJcUSN20KijNHmftlpKdJbk6OL26te1ik0GemXL0bGRS62/cGhe72r0UK3e9ft0Ih/+75yEc+In/84x+X1YmDg4Oya/ceAeCoH6SO0BdrqgZheFiYlJaWSFRk5OTW+LGyulr27evSr/m6w9mg0BdetD1MvNrl74BBocsdLKLCv1FRUT7XPHO/5QLjCd0KhVifKOGll166bClkfh7uBAhHRrTDmE5jX6ypGoSAIJIzYWFhk1sPDg1JeXmF8DtSNCpaHR3ti1sfsIdFCn1u0tW3oUUK3e1zg0J3+9cihe73r5uhcDlTyEP792uEkHF8aBASqfPFmqpBqPWBxUWaOnYWkUEihPgREGRs3lRg9MUZnD0MCn1pzVW6l0Ghux1vUOhu/xoUut+/bobC5Uoh798/LLv27BZ+Z0oJ00p8saZqECYnJSlo0lzCQpewobFRmppb9M+kqqkfdL7vi/tP38OgcCmsusr2NCh0t8MNCt3tX4NC9/vXzVCI95Y6hUyqeOeu3UKkMDEhQTt9fQFm9Q0AX7O+gNO7l6fqDyJUDSxO70BeijfXoHAprLrK9jQodLfDDQrd7V+DQvf71+1QuJQpZJpJSBnTXMI0EVK33gKhSs5UVUlXV7e+fNMnoKB9WF5ZpWlqRvdRPzi14WQp31iDwqW07irZ26DQ3Y42KHS3fw0K3e9ft0PhUqWQkZtBdgb5GWr9gDNvgZAOY6afAJlEANlzquRMc0uL1NU36EuZkBAvRQUFc+oPsmd9Q5MUFXpf42hQ6P6fB0v+hAaFS27iFb2BQeGKmn9Zbm7dx8ti5hW7iduhcClSyAAh0bqenh6dKVxWUvKOecMLdWhPb6+UV1SqtiGNImtKSyRyQnKGrzHfGFFqwJMJJvOZjsL1L7z4svT29cnWiy5Y6JHecb1BodcmtA0MCt39DhgUutu/Fil0v39XAxSiVVheXu4TIWsAbffevdLfPyAxMTEKb0T1vFnt7R1SXVurzSPR0dEaIQwLDdUtkaMBFon4AYukqOcjN1Nb3yA7Xn1V+vr69XOXXnyhN0fUzxoUem1C28Cg0N3vgEGhu/1rUOh+/64GKPRVCllTxrv3yMDgoERHR8nasjKvgBAIrK2rl9a2Nn3RSAnTuexAJl/n+1xHirqoqFBCQ0JmfSnx59u7d2vzCyCJbmFaSqqcevKJXr/MBoVem9A2MCh09ztgUOhu/xoUut+/qwEK8aK3Xch0/O6mhnBwUKKiIhUIvZknTJMKEcDe3l59yaaOw8MnpIs79+3TdDHdx1mZGXO+jPw8fuXV1zxRx7FxCQsPl4y0VI1obj5845yfn+sCg8K5LGTfn9MCBoVzmiigLzAoDGj3zevwVlM4LzMF7EWrBQq9SSEDhNplPDSkQLimrGzOiN1sLwSNJDSUEMkD+pCUQYeQxff2VlQKP1uJ8iFxM32+8Ux7d3f3yPMvvSzt7e2ClCH1iMAkncnaoRwV5fU7alDotQltA4NCd78DBoXu9q9FCt3v39UChYtNIQ8TIZwAQkBr7RrvgLCru1sqKqt0Asn0kXSIVVfX1Or3AMGiwoJ5TSepra+XV3a8Jn39fRIcFKxp6LTUVG2CKSkq0vv4YhkU+sKKq3wPg0J3vwAGhe72r0Gh+/27WqAQTy40hYwWYHllpTZrREZEeIDQC8BqbGrWKSSs6KgoT0NJWJjWDNbU1kpbe4d+j1RxdlbWnC8fNY5v7twpe/aUy/7h/ZrOBgapPyQdTZeytzI5Uw+xaCjkXxSIKs51mLKyMtmzZ8+cD24XBK4FDAoD13fzOblB4XysFNjXWPo4sP031+lXExQuRMh6aGi/7N67R0fXAYRrykrnFbWbyd5TawT5PtNHSBnTUMLPUMBzYGBQU9I0kwB1cy1qG198ebtOPRkbHdOzAZNEM9EvZNye5z/quqSuoUEOPWT9XFvO+f1FQeEjjzwin/zkJ+Wxxx6ToqKiWW9iUDinDwL+AoPCgHfhrA9gUOhu/1qk0P3+XU1QON8UMnV9CFNTS6gp47LSRUcIiTbuLa9QaRkWEUCnaYRGEhpK8AEyM8jNAHdzrdbWNnl5xw4hFS3jnvrBzMwMiZ5SP8ielVVVsqe8UsZGR+W8c86aa9s5v79gKMTgV155pXR0dAhFnQaFc9rY9RcYFLrbxQaF7vavQaH7/buaoBBvXnvttbJ161Y57rjjZnQuE0oAQlKzaAaiQ7jYLuO+/n4FQuCSqCBNI4zDI11cV18vLa0eKZqM9DTJyc6eM7vKtW/t3CXlFRXS1z8gISHBCpOaMo6Pm6wfpCFmx6uvSVt7O+qC2oF81JFbvH6ZFwyFH/3oR+Xcc8+V7373u/KrX/3KoNBrFwT+BgaFge/D2Z7AoNDd/jUodL9/VxsUzpZCZq4wXcEAobeTSmgaIQoIAFJOV1ZSrBE9Oo6RoiFyCGySRk5MSJjzReNzL7y0Xdo62mVwYFD3jI2JkeTkJMnMoH7QA5WMwnv9zbe0izkkOETKykoUFucq55vzAAsVr/7DH/4gpI5vueUWOfbYY+Wuu+46AApnqh0877zz5K233prPWeyaALUA9UgJCQk+eSED1ASuPjapEcAwNjbW1c+5mh8OHbWIiIh5pbVWs50C9dmBlq6uLklM9NSguX0RqPjYxz4m99577wGPypg5uoKxR1xcnBQXFiz631v1DY2TgtRoBLIXANjd0zOZLkYqhvrB8HmkiwHMV159Xfr7+xUqkcWJiY7R6CBQSY0icI+OYk1dnf5zVGSUHH7YoZKY6AHO+aSl5/L9vCOF9fX1cumll8r9998vGRkZM0IhTpi+/vKXv8jzzz8/1zns+wFsAaCBbi1f/FdKAJvBtUfnh48jreDah1zlD+akvrwd5bXKzei3jw8E4WNfQIPfPuS0g23btk2OOuooTQ+zAMK6+obJySGL7drlZyHyMHQrs2j2yMrwiE43t7RKe4enuxiII7o3n38vIkRdXVOnMMj+4eFhEhsTKwnxcZKXl6tNMEP798vbO3dJV3eP7p+SnCTrpnVKJycne+2eeUEhh/zQhz4kxx9/vFx22WV60/PPP19+9KMfySGHHDKrYKI1mnjtI7/fwNLHfu8irw5o6WOvzBcQH7bu44Bw06IPudrSx9MNRRSusqpav5yakiwF+fmLsiU/C0k98zuwV5CXJykpyUJghAhkb1+f1hU6kb25boI+4svbX9G6wMHBIY00Au5E/tJTU7U+kYBLS2ur7HjtdYXG4OAQWb92jeobLsWaFxSSWti8efOM97/xxhvliiuuOOjZDAqXwm3+tadBoX/5w9enMSj0tUX9bz+DQv/ziS9PtJqhkNnCNbV1as709DTJy8lZlGlJCwN+1CICanQRU+/H1wFOp4u5tLhISzHmWkQUEaNGdkYl/iLCJSQ4WJKSkiQ3O1vycnMUPN/auVP3J9obHR0jR23ZPK/pJ3Pd/2DfnxcUzvThmWoKZ7rOoHCxrgmczxkUBo6vFnNSg8LFWC2wPmNQGFj+WuhpVysUThWSnioTs1D70dhB6pnlGSlXoinehsYmaWxq0q8zwq4gP08jhXMtxukx5m5sbFSjjOHhERIcHCQpyclSWlys0Ucihy9u3661oCxg9rBDNxx0f2B1sR3UU8/rFRTefffdUlhYOOvzGxTO9XoE/vcNCgPfh7M9gUGhu/3L0xkUutvHqxEKqftraWlVx+bn5aqky0IX0Tm6i0k/s+ggJm2LPYkaUqcIBObn5irIzbUQy375lR3S0dmhe7CIOjK2jijmmtJS7Yhubm6WHa+9IcMjnnp9mkmYcXyw9dauXbLtiW3ynx/9yFxHmPP7i4bCOXeeuMCgcL6WCtzrDAoD13fzOblB4XysFNjXGBQGtv/mOv1qg8LqmprJcXJAHFG8hS7SwegPokPIAsqyszK1bhAgJMJHmph0MTI0cy3qBrfveFXrAsfHRWFyfJymknAVuwYIw8JC5bU33pDauvpJCN2yebN2Is+0kKS5597fy09//CNpbmqS8sqKuY4x5/cNCuc0kV0wlwUMCueyUGB/36AwsP03n9MbFM7HSoF7zWqBQiJ71N8xRYR6PBo15qMPON2z6AsChIAf8AZYsk9Tc4vONeY+U8fYzfZmYHu6hqtqPHqGoSGhMjo2pkAYFRUlJUWFkp+XJ+gnki7u7x+QoKBgKSkulHVr1hx0a6Kg1113nfz5kUf0mty8PNn25DavX1KDQq9NaBsYFLr7HTAodLd/eTqDQnf7eDVAIcCFYDRj4QA5InhoES50TR1LR92g1g+GhSlssjewSRPIfNLR3d098sqrr0lPb4+eic5iT6RwXKeeHHrIISppA4Du3rtXU8pEHbdsOlwbTmZaXPOnhx6Wb954o7Q0N+u+Z517rpxz3rvlgvPOWejjvuN6g0KvTWgbGBS6+x0wKHS3fw0K3e9ft0Mhz0fjRk+PB74YW4eg9EIXgtRNzc36MTqL6TDePzyssAnMkerla9FRUbNu7YlYVk2O0ouMiJTgkGAVpmZlpmfIYYceov/80is7pHOiZpHZxps3bjxow8i+ri75yn9/RR55+CEFyIzMTPnAVVdJUVGx5GRlyqEbPHt6swwKvbGefVYtYFDo7hfBoNDd/jUodL9/3QyFdN2iHUj6le5bgNARrJ6vZ53GESKBLJpG0CBEzsYRvCZ9jP7gXB2+zFV+9fU3tKYxOChIo5WDQx7ZGSeCWVZaqv/e3P7q6zJCM0lIqBy6Yb3kziKX87fHH5cvf/FLWjvIPqeedrq8+8ILJT0tTbuWx8bHVL/Q22VQ6K0F7fMGhS5/BwwKXe5gSx+73sFuhUKaQXbvLRdAjC7dtWWl82r6mOpwIoBAJU0bpIZzc7IlJSVFqqqqhcgcX2P6SUZ6+pzRwbqGRtm1a7dCYER4hCQkxOuEE8CV1PHmww9X8ezX3nhT6uo9zSTx8fFy1BFHHLSZhOjil7/8FXngvvs0Opialib/8qF/ldKyMu2qZtXXN0hPX59svfB8r99lg0KvTWgbWKTQ3e+AQaG7/WuRQvf7141QSBPIrj17PcLP4eGypqxUIsLDF+RMJGVIDTsaf6SGidqVV1ToWDlAjq/FTIzKO9jmg0ND2kyCZqFTL8iZWlrbRGRcxaaPOepIbVz5ZzMJjTBFOqruYKPwnnnmWbn2mmukqbFRo4MnnHSyXLR1q+TkZEtSQoLuj4bi/v1oHYbJ1osuWNDzz3SxQaHXJrQNDArd/Q4YFLrbvwaF7vev26AQYNu9Z6/W+SELQ4RwoXOdW1vbdIYxEEdzR1lJsU4nQQ4Ge8XHxUkRY+ZCQmZ9QZh3vGv3bv1seFi4pp6J7jmp6JzsbNm08TDZW1Ehe/aWT2km2aRNJjMtopbXX/9V+d977tHrk1NS5P988INyyIZDpSA3V+sca+rq9B6cLy4uVkWvS0uKvX6ZDQq9NqFtYFDo7nfAoNDd/jUodL9/3QSFABMRQlLHSLpQQ0jqeL4LCKyurZX29g79CF3A1AoCg4hUE7VDkzArM2PWLYnO7S0vV7DkLHGxcZKclCiNzc2T9YOHHrJe084vbn9FO/xZmRkZCokHO/MLL74on/30Z6ShoUHPctyJJ8rFl2yV0tISBdXKajQY2zW6CcwCiRmZ6dLfNyBlpQaF830P7LoltIBB4RIa1w+2Nij0Aycs8RFMkmaJDbzC27sFConAUUMIENFdTHRvrsaPqaYH3kgXI0DtABrROsSo+TkHqKFtSLp3tgWLZB3hAAAgAElEQVSUUYfY0dGp9yc6GBkRoXWCnI3o5VFbtsjQ0KC84jSThIbKhvXrVc5mpkXU82s3fE3u+u1vJ6ODV7z3/XLkUVukqKBAOjr36f6Iaes9k5KkuLhQRoZHNErJ2rJ5k9dvmkUKvTahbWBQ6O53wKDQ3f61SKH7/esGKOzt7ZM95Z70Kx296BDOZ86w492BwUGN7BHh43NEB/nZhgwNCxBEpHq2NPTwyIhUVlZJXUODikzHxcZIcnKyUFPY0tKiqeiUpGQ5YvPh8vau3ZPNJAkJCQpsB5Oy2b59u3z6U5+W+ro6kaAgOfa447V2ENkaNBL3VlRJV1e3PntMbLQUFxRKfHyctLR6xvghecOYvLTUFK9fZoNCr01oGxgUuvsdMCh0t38NCt3v30CHQvQHicwBXUjDEM07WHPGTN6kixjxaewA9OXn50lzU7NGDD3p4oxZZwvr35GuLhWZJkoo46L1gPxqbm6Vrm5Pl3Jhfr7Kyrz0yivaEa1TVYqLZF3ZzM0kNJ7ceOONcuevf6NnS0xMksve+x454YTjpaigUOobGqShsVmG9g9pEw3QV1hQoOd2NA+RpOFXRMTCmmwO9tYbFLr/58GSP6FB4ZKbeEVvYFC4ouZflptb+nhZzLxiNwlkKATGSO8ChMwwJpq3kNXY1Kyj6VgIUjOejj8zag5ALC4slNjYgwtdkw6mBrG+vlG6e7pVA5E9YqKjpKqmVqON7MN0ErQSSW9DjdT7IUGTkjzzZJJXd+yQT3zik5PRwaOOOUYu3nqZbDlikzbQALFEI9EfBIQL8nIlIjJyUuia9HlWRobK3rBoOqE+0ttlUOitBe3zplPo8nfAoNDlDjadQtc7OFChkMYP4IjFWDlHl28+DuOZq6prdA6y5/MpMjw8ohE/ljaYFBbM2l1MrR7p4ta2dhkeGVYY5HMjoyNSV98oo6MjmspGNJrmly7dO0gy09Nl0+EzN5MQHfzWN78lv7zjDk+Xc0KCXPG+98nxxx0nebm5Ul1Tp2cmOogUTmZGmqSmpAryOdREkvqmeYXoJpFIvkYKnOjhhvXr5mOaWa8xKPTahLaBRQrd/Q4YFLrbvzydRQrd7eNAhEKmidTU1qljqJfLm2Xax3TvAV6kevsHBiQkOFjS0lJ1wggA5RGjzpaM9LSDOh170Y2M7iCARuMIMMg84rb2NmltbdfPskdqSors3L1b96ZR5ZD16yX/IM0kr732mnzi41dLHbWDNIYcdbRsvexy2bBhvUYF0RwcHBySkJBgSUxMlOzMTBhzMlVMpDQjI32yNpFUdn1Dk05FAXiPPfpIr19kg0KvTWgbGBS6+x0wKHS3fw0K3e/fQINCYKyhsUkdwzQRZFzmu4iokW4G0oA50rieCJ7oP5MujoqKPOh2RNyYW0y3b39fnyQkJmpDSWxMrNTW1WmnL+liagep6wPkWEQRj9h0uMrkzLRuuOEGueO22/VbCQmJcskVV8gJJ54gyZrOblIYBGZpIElPS9UoIZ3GLBpUgEGgkDUwMKjRQWoZSTUDujzr5sM3ztdMB73OoNBrE9oGBoXufgcMCt3tX4NC9/s3kKAQ3b+WFk9XLeli0sbzXdQKUkOoIBUdLSPDwyr0zCKqR4TwYA0q1CzS2MHniQ6GBIdovR6QNjo6pt9DIxE4JHLJn/nZGBQULGtKi4V5xjOtN15/Qz72sY95agdFZPORR8nlV14pBfn52owCxAKEkZERCpbcD3/xy0kVZ2akT3Zacz6gmS5quqGpXwQaQ0PD5PDDNszXVAaFXlvKNjioBQwK3f1yGBS6278Ghe73b6BAYV19w2TkjYYSJzI2l4eIChIdBLCCgoMlMjxCBgYH9GOMmysqyJfYWbQHgTM+T7NGd3ePxMXHKWihP4jINZA6Ojaq0BYcEjyRPh5X8ERqZqYGD35uojv42zvv1HPExsbJpVdeKccee6wnetndrSlfoC4xIV7PFxYeLmOjo3r99FQxEcrGxib9XG9fvwQHBen9w8JCNaoIQNpEk7neFPv+sljAoHBZzLxiNzEoXDHTL9uNraZw2Uy9IjcKBCisqKqSzk5PUwjzhum4nc8i3QvQkXoFjIKDgrURhJWSnKzRxoPpGRIdbGom8tassAVccl8gi45k0ro0uzAPmT9zL9K1FPoV5OdpY8dMez/77HNy7Wc/K410PQcFyZYjj5JLr7hCUlJSNLpIRzORvtiYaAVQtAiJYPKLrmIaVRITPc/PtUQGOWNfX792TZP+RqIGbcWx8XHtemaZePV83hi7ZsktYFC45CZe0RsYFK6o+Zfl5gaFy2LmFbuJP0MhkFNeUSE9Pb2T0a65Joo4hgToADfgjsgZgMSi4QPNQEeuZSbDIzgNTPb29sq+rm4FLaKDyclJMrx/WIWh+TrgNjY2rk0rRPUiIiJly6aNKlo9fRFxvP666+Xee+7RbyUmJcmlV1wpm47YLDI+rmloooNhoaF6NppggkNCJDw8TOsU6Sqe2gADkPJ87R0dMjS0XyOMSOF47BMkPb2eSSY8L93V2VlZXr9jVlPotQltA4NCd78DBoXu9i9PZ1Dobh/7KxQSmdu9Z68wbQSwKSstOejUj6keGhkdVakYUqo8WxD/Cw7SS4AtgHC2ecjNLa2qVUgjx0D/gDBxBDBDBJqOXn5RPwgkcg1Q6OlazpKNhx6q3cHT1/33PyBfv/FGaWtt1WuP0akkl0p0dJRG+/ga8EpNIvfiz0BeUJDofYFBUt0sfuYSGaSxhfuHh4VrpDI+Ll7v3dc/oHI4RCmpuQQIaTTxxTIo9IUVV/keBoXufgEMCt3tX4NC9/vXH6GQNCzafvwODK0tK52Eotk8AiQxv5h0MXN/g0KCNeLGr9zcHJWIOdgiZUtnMbWHTEkJCfXU45GyRdiayCPzjMcZWTIuMjA0qDqGnG/TYRslPf2dTS811dXyxS9+SZ595hm9bUpqqkYH1x9yiEYGQ0NDFCqZOEKUD6CNiozUyCC1iHQVT42MtrS2TdY3sh8wmBgPDIaqdiEgTZQwLS1FgZC9fLkMCn1pzVW6l0Ghux1vUOhu/xoUut+//gaFpGL37C1XwCEaR4Rwtsie4yHkX5BiIfIGFAJrRNwAOhpTnEjbTB4l+ldXVy+D+/drDR4gFhISop3EQ4NDmqLV+sHQ0EldQP6ZKN6mjYe9Yyby6MiofP8HP5Bf3HLL5FSTU08/Q04740wFQa1vDA7RRhBS02Ojnm5iGkr4M3WDNLI4i9nO5VVV0tLcIkP7h1UGh/rGkNAQTTmPjXkaUKiT5ExEIKcum2ji/r/HAfOEBoUB46pFHdSgcFFmC6gPWfo4oNy14MP6ExQSpSP1i5xKfFycNpUcrBHEeVAgkMkmgA+1dePjYxOpV09Kl1q8gy3uU1VVralmHRs3NqbRNyJ1SL00Nbdo1JC9AUxPujZM99+wfr3uP309/dTT8qUvfnFShLp0zRq5+NLLJT0jTcbHxhVOgcHw8AhN93JmooJEC526QYCUxXkqKqulqqZa9QeJ/MXFxUpkZJSKUjsLQES/kAkqUxepd4S229ra5fhjj17wuzH9AxYp9NqEtoFBobvfAYNCd/uXpzModLeP/QUKidZV19Sqsec7x5ioIulifg4BbHTdAnRE24oKZheiZqQdo+6IKhKJI7pG9A9AQ86FdDESNOyr6eiREYVBavQOP+xQ/eepC/C67rrr5NGHH9b6QIStz7vgAjns8E1aG4hWIFDHGZGuIQIZERmhdYSpKclaNzhV3LqhqUkqKqpUF5FzcaaEuDgF5uCJGkkii8AgcjhTl2eMX63OZUZEG7A+96wzvH6RDQq9NqFtYFDo7nfAoNDd/jUodL9//QEKp2oQZmVmSnZW5pyGpwOYz/EzCIFnImhE84jw0Wl7MCFqIouMyCMdTMMIHc7UDrKI/AGIACPfZ28ieezF/mvKSrVRZeoCAO+4/Q75wfe/r1FFAOz4E0+Sd515lopOq5RMdLSmwoG54ZFRTXEjKwPMAYNTJXb27evSMXxNLS0Kl8An3+efnSYWABE4nalGkmcDrp05zjEx0WqPdWvK5rTpXBcYFM5lIfv+nBYwKJzTRAF9gUFhQLtvXoe3SOG8zBSwF60kFGp6tKpKuro86dnCgvw5RamBOFK+RNAAOECLZhAVoi4s0BrCgy1AqaamVieZTI0sAmxMNKmurdE0LbOVaTwZ2r9foiIjJD09XQ5dv17BcOp648035fPXXCs7d+7UL+fm5csll18m6RmZeq6w0HD9DKnhkZFRjdqRFmdOcmZ6mtYsOstpriHdCzR6opZxWtvo1FTODoP12pEMzLJiomMkNydLG2x4Pl8sg0JfWHGV72FQ6O4XwKDQ3f7l6QwK3e3jlYJC0qA0lKDfB/iUlZQIUa3ZFuniiopKBTpSu7FxsVrjR8QsLzfnoPWHdPXWTkQHgS/uDSgBolmZGTqODhkazkIam3Qx8Ekkr6igQIqLCg9odkGo+lvf+Kb87u67FeCiY2Lk7PPOk01HbNEz0O1MfR+AOjwyrNFGvs5+REGpHUR6xll7ysulurpOJ614opJxE6nw0AnAi5bUGSKDpLRr6xqkrr5+MjLIPZm9XFiQN9kAAzxTK+ntMij01oL2eTEodPdLYFDobv8aFLrfv1OhELHm9vZ2KSgomPXB93V2yn333SdZWdmSlZ0lmZmZGk2b7wK+9pRXKHxFRkRIaUmJRtNmW0TviKIhZL1/eL8kJiYqEDKmLj4+/qAfZRJKTV2d3ovGC8ShqTvkfrnZOTo6D8hjZF13T7fKwjDbmFTy2jVl2tE7df3+93+Qb3/rW/rvNgBuy1FHyZnnnqdpXiamUM+IHiL6iNyTqCSQl6tNL2kHjNQjzVtVU6OA6zS50EQSOWELon0eGDzwDEQzGxobpLa+Qe3BiouNk9ycbCktKdI/A79EYGmS4ZdNNJnv22nXLakFDAqX1LwrvrlB4Yq7YMkPYJHCJTfxst+ANObu3btl967dsnfvHnnj9Tekqrpampua5KijjpK77/ndrGd6+aWX5YrLL3/HNbm5uQqIgOIRRxwhH/jgB99xDQBUXlk5CUGlxcUaKTzY8jRN1GgEj/QvQsxEw+YSoiYaSKqYzwBmoxONIoAcGn5AXH1Dg8ITYtD8zgxj6v+A1NLiogNkbHbu3CVf+fKX5eWXXtKjpqWny6WXXyGZOTkKgzSPUPuHXAzQxlQUmkoyMzMUMB24pDaQ+1VWV6vuIZNWAGOaUJxIKelwop/TYVBnHDc1S3094tqMrwvSFHNubrbWOvJsDgR2dfXI8PB+jVIiWXPi8cd5/Z5ZpNBrE9oGBoXufgcMCt3tX57OoNA9Pq6tqZH3vfd90tDQcNCHOu744+Q3d94560OXl5fL7bfdLo2NDdLY0ChNTU3S1dV1wGdOOfVUue322w74mtMcAhgBScwIPlhDCB8ErgDIzs5O6e3r1+YM4IlU8fQI3tQbqe5gfYN2DPMzipo8fhEhzM/NkbaODo2iAahcCwwS2UMb8LANhxwgYwNk/fhHP5Zf//JXMjQ0qKB4+llnybEnnCDjYzJZ05iUlKgABlzyTABicVGB7kXqmGfmXhVV1RqV5GzAMB3HgB0LGExLSTlAo5Cvo5PY3NwiTS2tk93EaCnm5eVqBJL6RwcGnVnHRCnZH3FstBEtUuiev8cB/SQGhQHtvjkPb1A4p4kC/gKDwoB34eQD0G27Yf0h+ufi4mIpKS2VtWvXSlZWpmzavFnWrVu36IflZ0FdXZ00NzUrdCanJMtpp502uR+pUqCIReQsMyNDamtrpa62TgDR6cuRqHGmiFCPR5q4uLDgHWLRzmeJzlVX12g6mEghotBOWpqoG5+nO5fr+HcT1wFrEeERUlhYIIesXTMpNUOq+cltT+p4urpaj1TO2vXrZetll0vEROMGgAj8AV1AGELSQB4p7ezsLAVYhcG2dqlBL7C9XSGVxXWJCfEe0Woig6kpB4Au+7V3dEpLS5u0d7arjiKQR21gfm6epKYm6xg+YJBoKPdh8SxELUnRs4iSErE8YtPhi/at80GLFHptQtvAoNDd74BBobv9y9MZFAaGj4mm0dU61yJtvGbNmsnLlrrRhP2J9hGVA4Bo3CDix/r+974vN990k2RkZMi7z3+3XHjRRbJhwwaVVKHxY19Xt8TGRCvMIatCTd5Mi3uQVqU+EDgiCke0DoiihjA/L0/BiYgbTRfUJwJdnIdu4MM3Hqr7s4BJmlm+8+1vy+N/+5vul5ScLBddcokUl67RqCL7EtVDN5DoIM0kRCKB3YK8PE1t87nWtnZpbGqStvYOnZTCYlYx36fRZCYYJLUPDAKQAF9/X7+EhYdrY0x+Xq5ERkWqlA6RTgcwOQ/QTMdze8c+nX2MTI+m5YNEbWCRwrn+Ztj3l8UCBoXLYuYVu4lB4YqZftlubFC4bKZe1I0qKirk5z/7mdx7z73y4MMPyfr16xe0z1JCIeC1e2+5QgzQVFZSrCLMziIte+stt0ymnvneCSefIps2b5L0jAxBs5BIHFIz08WinT1otGDiBylUYmVEBx09P1LMACjRQU9ncYdGB3lmmlToBN5yxGb9ZyCO2cK//e1v5Ze33TapOXjqaafJKaedrnvzf5wjHmmaIJo5hhU+k5MSpaS4WKGVGkEig4AnUIh2oUdjMEQBFJFsRKepGUxJ/ifEA3ntnZ3S0QFA9gud1kQigUE0Cfln7MjUF2fRwEK6Gekcj4zOfm2moZsafWvP9JQw/Ty29HZZpNBbC9rnrfvY5e+AQaHLHWyRQr918LPPPCt33H67/PWvf50849Wf+IR85v9+ZkFnXiooJOKFCDORN0AKIDzY/GGe5fHHn5Dm1laJiY3RNGxba6uCzXXX/T/Jy8t7xzMBnLX19UJ3MYtmD60NDApSACVi19Pbo6CnXdUdnQpPRAdpJtmwfp3CJovvbX/lFfned74juyY0BwsKC2XrFVdIckqKMMsYuOI5+IUMDXbjn2mUQQ8Q6CO6BwhyJuCNMwKERDqJCsbHeyAueQIG2QNdQe4PPJIiJvLIGDz25jM8C6DnzDfGhqTCaZbhs62t7TI4NKj1l1BrUHCwNq54rktRIJzP7Oj5vDQGhfOxkl0zqwUsUujuF8Sg0N3+5eksUug/PgYiHnnkEbnlZz+X119/3QNDwcFy2umnywc/+EE5/oTjF3zYpYBCol6IUrM3DRGlJcUH1RAEmkgXM7+Yjtr9WhdYJY89/Ig2sLz48kvvgJrW1japb2xUOAPGxmVcI4QsRuQBTVU1tZqyBbjYd5T6wgmg2rxpk3YJk56lIeUXt9wiDz7wgO4XExsr551/vhy+ebNqFRISpDYQSAsS0a9xz/zcXCkszNdIngODgF13T69G9HguIp+AHRFBagY5Gws4pVaSdDY/QwFoxK1DaIgJCdHUMnAnE3WCfAYJHp1vHBur4ElkkOgnMEgzSXCI55zMVE5LTVYg9BUMOi+VQeGC/3rZB6ZbwKDQ3e+EQaG7/WtQ6D/+ra+vl/e9573azMEidfie97xH/uWDH5CcnJxFH9TXUEhdH6DFAkyogztYhzE/P97etVvrAcfHxiQxKVFys7NVbw/YbWxslKyJWj/2A7aQciGixp5AHoAFgHmig7nS1z/gmVvc06NTT/ZPCEcj91JUVCjryso08tbS0iqPP/64/PTHP5b2tjbd7+hjj5XTzz5bYW5keFTr90gto1sIeHINKemy0mIFPOAMIOQ8ACEQSvqYZg8inhlpqQfAIKlrDwx2auSPFDEpafYGPoODgiQoOEgjfazoqGiNKjL5BCAl/Q0MApHAIJqKoSFoI0apVI8TGZxN4mfRLwonHHfaWbzZZZbPlpWVyZ49e5Zod9vWHyxgUOgPXli6MxgULp1t/WVnixT6hyf41/GpJ5+i9Wgf+NAH5eKLL1YQ8Hb5CgqdiB/RLxZTNQ7WGML3O/btkzfeeEsFo2m+SEtLVW1AYHf64ow0npAKduYBA1XU9LGoO8zISFddQmAQyRfAj8gfUbekxCSVmmECCjC4a9duufXnP5MXX3hBP5+RmSkXX3qp5BcWasQOwCT9SkraqU8kUri2rFTrELURpM2TtkUqB9gbHaFxJUQjg2gTpqelaa0hq3Nfl9YKOvOIqf2ToCBNFXPG8bFxiYzyaBU6TSNEFp2ZzNwPGAQ6AUnS2VxHfWJkRKR2IgOESwWDjj8MCr3922aft5pCl78DBoUud7Clj/3KwfxHdlrazB24iz2oL6AQsCmvqNQ6OiJ8xYWF2mE70+J+pIrpSAaOgCj09hBfnglq6Fpm6gf1ecAa6VqnWYQ/P/H3v2ua+bQzztDvA2BO9zHRQbqK15SVarcuEcT7/vAHufd3v9O0LVB92plnynEnnCTBdOqOUycYpeBJJy/n4Rf1iUWF+dLT2zcJg8ja0MnM70T4ADpkduhARrMQm2hUsLNzsvOYfXWyysCgSsUEBYlGJXkmYJgOYmoAnaU1g23tWhNJNFK1DUNDFBaBVCcyiM2XYxkULoeVXX4PixS628EGhe72L09nkUJ3+9hbKATsmGEMHCF9UlZaounMmRYw99rrb0pHZ4d2yFJrB7A5tXZTPwM80TXsRNcS4uMVpBz9Pf7M3OKPf/xqCY+I1GhfWka6pKR4ImzU4AGnwBNRtjdef11+fPPNk+n3DYcdJudfdLEkJCRo6V5oWKhH7HnU01QCaBGto0EGGAPO+HlHJJGOZ+YvA45cS0S0sCBfoQ4pGJ6P6J5GBLXuM0QjfP19HojkMzHRUXpGPkMN5NTuatLeTucyMKhAHAYQewDSGX23XDBokUJ3/wxY1qczKFxWcy/7zQwKl93ky35Dg8LlMXl3d/esM3yX6hTeQCHSKXsrKhSaAEEACuCZvoiQ0fixZ89enVtMahbtwJKiwhmvb25p1XSxdvgy1i4u1jMSbkqTB/esa2jQSR8VlZX6Hy+sHuwYFytnnXWWxMXHS3Nzs/z6jjvk8b//3aM5mJQkF192mZSqVmOQ1guGh4UqcKquYViYghdwyzkdwWk+S6QQGKT+kfpCUsQlxUUKt0RJnXrBcUadTHRE0+RC8wmRQyKZwGB2dramlqfDMAAMDO7b16XwS+c2oE2amIgincsA4WxTYJbqPWFfixQupXVXyd4Ghe52tEGhu/1rkcLl8e9Pf/JT+dGPfiiP/eUvBzRWLMfdFwuFgAsdxh7JlTgpKSqascOY5pAdr72uTRK0VCTEJ6gcjCPLMvUZiYqRKgaINFKXkqwQBnyy0PnLyc6W2ro6aW1vVwgjGkfEjgheZXm5vPbaa9LX2ysJiDkHiWx/6SVNvwJ8J516qpx6+hmaNvaIWzN+TmRkZFgiI6J0MgmwmpSYoBFKfr7x/f4BzkD61lPDSLMJcjZEKknxcg46mT0rSLuGe/r6tPmExb0BQBpoAEnqHKcuPgsMUnfYPzAow/uHJTyCaGK0imQ7c5BXCgadsxoULsffSJffw6DQ3Q42KHS3fw0Kl9a/jIP7zKc+LS+99JLe6Lvf+x9tIFnOtRgopFuYSB4LyGEW8UyLa9546+0JcAvRWcc0a0yXSuEM9Q0N2kjCiouLldiYWJ1Q4kQH83JytEu3qrpGpVxI4QKOdOsCT9QmUg/Y0tIsDz/4kDz15DbpnpjHXFRSIhdt3SqZmdk6Ak7RLShIO5PRBCQiiNwL2n+qFbjfA4P8zp8BW4XS+DhNE+dkZWl6GBgEGAFjFc4eG9NzOSluIDMjPUM7sAHc6YumGJWXaW3T9DKNM1GRERoVxAYODC7n+zDbvQwK/cUTAXwOg8IAdt48jm5QOA8jBfgllj5eGgc+9OCD8qUvfkmjSRsOPVRuuvkmKSwsXJqbzbLrQqBQ08DVNRodYwF5gMv0xc+FHa+9Ia1trfotUsubNx4mycnvBCPq52rr6rVujtRtZnq6RumcyR0aHczJlrq6eh0Zx/WIWzPTmLrEhPg4kaBgT/RtfFx+f++9cv8f/6jpWur0zrvwQjnq6GMURAFB4M0RlaY5hJrC9PRU7eh1agCJOhKhBO6wj2fEXJ42kWhksLNT9/BEKUP0XjyzppbHx/W+WRkZUlRUMNlBPNVGPBsw2NTUrPdAVgewJU3MeQDImeosl/3lmHZDg8KV9oAL7m9Q6AInzvIIBoXu9i9PZ1DoWx+TyvzKl78s9993v0LKh//93+Waa6/xudDwfE89XygEfKgfpOOWCB3pYiJn01dNXZ289fYuTbXyfHm5uZount5ZTFSsurZGZyKziNJRP9jQ1OQRpQ4OVlkbInt7y8ulgykhPb3afYs+ISng0JBQhTZqDl9/9TX52U/+qTl45NHHyDnvfrfExcVrmlilX7T7d0SjgzSqkAYOCw87AAY9YtLU8w1LZGSEdi8jl0MKm/QuexA5VBgcG5PRkRGFQZ4VyMzOzpL83JwZm22cucsIb9OBDFgCggAhDSc0yZC69tdlUOivngmgcxkUBpCzFnFUg8JFGC3APmJQ6DuHbX95u1x99dXS3NSk0jI3/fBmOfroo313g0XsNB8oRE9vT/neiRFsYbKmtOQds4j5WbD91dekvb1dT0F0bfPhG7WxY+oCqmgkIernjIoD/lpaWlRjkMXUjty8XKmtqdVRdnxdm1kiozSaiKC0js+LiFD4vO3WW+W5Z57Rz2ZmZcnWy6+QwqIiBW3gLkiCZXh4v4IbOo/oGpJuHhkd0Wkg7M3Ek4FBT6oYGATQkhMTtQGFaC4wyXUsIJPoHvDIeYBBooik0pHBmb4Aypa2No12enQGRzxSNDSPpDIDOXlGwF6EO5f0IwuGQsKgOGGm7qOZTmri1UvqP7/Y3KDQL9ywZIcwKFwy0/rNxgaFvnMFs4pv+OoNcvY5Z8s3v/WtFek2nv40c0Eh0S0ihETagBhG1tERO3VV19ToZBJHHx7gsokAACAASURBVLAgP1+jg9MbI4iokX72RNqCVQiaCCITUNifr9GMAfS9/ubbmiqGK4jsAXOeqW9A3KhC3V/+/Kj84X//V/ejLvDMc86Rk099l/6zRyBaZHRkTOEzKipSYRP9RM7FHh6pmTYPXI6Oako6JjpGoZEqQe6NxIzWDE6khQFHFbgOCVEwBuqIclIDOH0BjWgjkh4HBjmH1j/GxihApqQkz5he9t0b59ud5g2FTz/9tNx44406koZ18sknyw033KC58dmWQaFvHeaPuxkU+qNXfHcmg0Lf2dJfdzIo9K1ntj3xhJxy6qm+3dSL3WaDQmrngDiACJhC92+qNh5TQ3YQHZyYYgJQbd58uCTGHyhcDfDRSEIdHYu0M+Ps6hsaJ7t2gbz8/Dypqqqe6EAe1Ggge5Hi9dTw0SUcITvfelN+9ctfSsdEVPLQjRtl62VX6Jg8ngfAQzaG9C7wBlAiUxMREamRRaJ+LL7/xONPyMBAv8AjmzdvUvAEKJlWAjw6kUDOouA6Ub9I+pm0Mr9PX6SG6xsbpLauQUfSsbReMD5BNQ2pGfTFNBov3L6oj84bCl999VV12JFHHqlk/fGPf1yOP/54+fCHP2xQuCjTu+dDBoXu8eVMT2JQ6G7/8nQGhe728cGgsKGxSVO8rMyMdJWCcRaQyAzi3Xv2arQNUCwqKJB1a9e8IzoIWJI2BaqIAFJjODY+psLUQBaLrwFvO15/XeVjBgaZNhIuKYlJMjA0pE0cAFpHW5v88vbbpKqyUj+XlZ0tV7z3fTqejtnAQCN7Q3ackQYXonJxsXGaRh6ZgMGg4GAZGqSmb0Refvklqa+rk9DQMA1kbdx0uKSmpmr6m1QwEIi2ojP1l2gjMEgN4PRFxJKayrr6xkkYJDJIejgjI01/n955HUhv17yhcPpDff7zn1el7i984QsGhYHk8SU4q0HhEhjVj7Y0KPQjZyzRUQwKl8iwfrLtTFAI2CCTwmL8HGlOZ5FOfu2NN7Txg1QuwHXEpo3vmFlMtK2yukYhD6ADpNJTUzWV6mj6AV15Obmyp7xc6urrPbOAx0Yn4Yl7cb6uri556IH75IXnntdjoEF4wUUXyZFHHaNpXu5F1C9IgrROkEYUgJA0MF/n+0AnqWrglD0ZTec0nzQ1t0j53j3S0d4hPb09OmXloosu0k5lR46GKGhamqf+b/ri5yDPWl/foGlinhcY5JkZfYe49UprDPridVsQFNKVU1FRIc8++6zceeedcscdd8i6desMCn3hiQDew6AwgJ03j6MbFM7DSAF+iUFhgDtwjuNPhUIyfswwpvYPgGJaB5ExFnBVWVUle8s9E0zovi0pLpQ1paUHAA8RNSCLWjpPLV+UFBXkS1//gIKfdhaHhGhjBpG71996SztxgS+EmqnNI+LHn/n1t8cek8f/9le9J7WCZ5x9tpx1zjkqEk2zB/t5agRHtAGEFDGpYiaV0CRCPSIpYM41NDikkUTup2nwcdGIZGRUlHb9Pvzgn+TRR/8sSUnJ2rBy+hlnyCGHrNd078Gkd8orqzU1zlk5B2nirIxMFbZO9ONO4sW81QuCwgcffFBuuukmqayslPe///2aQp46uPvNN998xxkQ6XzrrbcWczb7TIBYgH+hxMfHz6h0HyCPYMecxQL8FzhgyDB3W+60AJ2X1D/xL2Rbs1vg7rvuklNOOUXTmoGyADdG7OHj8sqqSfhCcgZgYqEbuHP3Hh2/plNJ4uLlsEMP0Vq9qYsu25q6Wo34AV1ZmZlai0iqmIghyzPrN0Xe3rVLawz5GTI2Pq5RPaJ51CkCp888/ZQ8+tBD0tfXp7B1zHHHydbLLleAA8DQFSSS52kCGfPU/kVFaYp6bFxUt5B/JpJIXR9n0jR0cLB+nWsBQZpEqHEEFKmNrKyskr/99a+aom5uapS7775bsnMO9CfXVtVUS2Njiwpcs5hLnJOdqZFBUtb+tubbADzbuRcEhc5GhHmvv/56pfcf/OAHk/t/+tOffse9HnroIXn+eU842JY7LeAIkrrz6eyp+IHsTBwwa7jTAk5XqBvSX0vpoZtvukl+9ctfyYYNG+S2O24PqP8Qpu4PmRj+PntSujl6flKtRPeYYEL9HRM6kI9Bh2/6+4D2XleXZ9Qb0UUiZaR/m1tblQf4j4rM9DTp7OpSSAQGieQR2YtEiHoi8vfm66/Ln+67T1pbW3SvktJSufJ975es7CwdNcdeTt0gMOk0frA/UAnI8s9c193bJ4MDg5pS5nmiIyP1P2BTU5O1gQUwBHg793lG2rFoeOH8995zj4Ls//3s/518bUgN19c3qryMI09DZJDmEbqJaYLx1zWTcPhCz7ooKOQm27Ztk0996lOyY8eOWe9p3ccLdUngXW/p48Dz2UJObOnjhVgrMK+19PHsfgMOGFX38MMP64VX/dtV8oUvfjFgoJAav6rqapWbmdpQ0tLaqrV+nuigaJ/AYRs2aGp26mI0HcojdPwSgaODGFHp6trayXFvCEATuXvr7Z0KhYyX86Raoycl7KqrKuXuO++UivJy3T4jM1Muu+JKOeLIIzWSqRHFMY+8DNqCRCzDwsJVU5CmkKjoKImKiJS+gX49MylwhdGwMO361SheZqYkJsTr59va26W9vUO7jPX5dJJIikY2py9qICurqhWOHRjkOuCZNPhqiaLPGwq3b98u69evV+qmtvC6665Twr7tttsMCgPz3wM+O7VBoc9M6ZcbGRT6pVt8eiiDwoObk9Tmv//bhzXjxaSNr3/9G3LZ5Zf51P5LtRkaehWVlTI4NKTwtuGQ9TpajdRoRVWl0H3M3++I8AgpKiyQoqJCnTLiLASlAUqnEYO0KalYOpYBLhZp2Yy0NKmqqdUmDDT+hkdGJSoiQkJCQ4URdsw3/sO998gLzz3niVTGxsr5F14k55x7rjZtUL7gmSs8qgLTXENNIlE5Pk+qNiQkVKed7Ova59EVlHH9fkZ6uhQXFkhKaopH8Hp4WNraO/R8zkg7xLWpGWSv6auzc582kHBGBwZJfzPrOTc35wB7LJWf/GnfeUMhGoU0lqAATt76Xe96l3z0ox+VnJyZh2Q7D2mRQn9y99KcxaBwaezqL7saFPqLJ5buHAaFM9u2ublZPvSBD8ru3btVyuSnP//Zik8nme9bABghOM1CIiU5MUFyc3OlobFRqmtqNaXKApgOWbf2AC0+/s4zZcRJFZNuLSjI10AQuoNOQwjC1ETraFxhP6KDpHCJqlFnDmD+7z2/k7/8+c+e7uDQUHnX6afLpZdfoYANkKnm4AgwSP3guM46JuLIpBHqGfk6c4T5BfCRgo6Ni9GO5rVlJZOj5mhIYdJKW1uHStOw6CIGBqfXRfI9oLGqulaFrR0YpIM4PzdXYXC1rnlDIQbCIbwU00fazGY8g0L3v1oGhe72sUGhu/3L0xkUvtPHb735pnzogx9S0CgpKdEaQqDK3xdRNur5nEgetXOFBfma/u3q6VUIImpI1g8AIjpInR4LAOP7gJ8Dk0wfIXULSDrzf4nOUddXUVml9YQ0eYyPjSv0cT9q2/76l8fknrvvlu4J+Nxy1FHynve9X1LTUmVfV7fWARIZpKYRMemgIEbLhSjIOdNHiNLy84drwlRjME4jmmUlJZNuIGrIs/LLo4kY5OkkTk15xyQR4JNGk6qaGgVSmIZFSrkgP1dnIE9fD9z/gPzlscfkuq9er0Ext68FQeFijGFQuBirBdZnDAoDy18LPa1B4UItFnjXGxS+02dXf+zj8sgjjwgKGgBBIHTfAznIyZCSZdEIQnMEmoRMERmcqPMjIsYoO1LJLECSLmHSwk7UDKjKysjQ5hRAkWuIuGWkpWraGXBkRJ02eAQFK4AhCF1bXSU05DTU1+ve+QUF8i8f+pCUlpZJb1/f5OxjJGnoKKbukOggTSERkYyiG9H0MIBH9zFAmpAYL2UlxZKenj4JsICtkyZWTcLgYIU7gBDgnbr4GQYM1tTUyb7ubk/EcUJXsTAvTzIy0g/6l/b4Y48TIsb4/5prr5X/8y//J/D+gi/gxAaFCzCWXTqzBQwK3f1mGBS62788nUHhO30MdPzi1lvl6k98IiBeAOr/kFqhGYSIW3FRocIPNYF0HpMKTkpKlOzMTI0OOrON+XrdhAYfD0pncn5entYRMq/YUZfgc8AmI/Fa21oVMFlE9QDIkf3D8uMf3iw7XnlFv0608JLLL5eTTz5FI4ykl2n+GBkeVvFqQJDoILOFAT8H1IjmAXicIyE+TqesALaOdA57tbURGezQRhSe1QODKdqQMnUhn6MwWFcnfb192gnN9dRFFuTnSXpa6py+RZv5S1/4orzwwgt67eYjjpCvf+PrsmbNmjk/G4gXGBQGotf87MwGhX7mEB8fx6DQxwb1w+0MCv3QKQs4EhE+oncsAIs0N+nijn37NE3KZA+AacP69QpwLLQCa2pqNXrHQsOQWcWRUZGaKp6cUpKaqkBGSpp6xJ7ePo0a0tRBNy+1g3f+6lfy6CMPa30gkHfWuefJhRddpGLYQJkT9dP0rkYGPaliOomDgoO0ISVoXCQ0LExiYqJUMoY0MjCIHAyL8wCCzgxm0snIzpDSZbrJ1EUncXtHp2f6SH+/wiCpbSCQ2sjUGSaWzGXue++5V775jW/of0BRD/nhD/+7fPJTn9TnddMyKHSTN1foWQwKV8jwy3Rbg8JlMvQK3sagcAWN78WtgSzq+ogSsoiW0aSBrAodvUTVdI7vhHgzNXPU5zGdA6kWFnCGADVpVyaUTGoZRkdLenqafq2GaGN7h0IecAW00Yn82KOPyF133qk1ikT3jj3+eG0iIc1MZNAZaTdGRzHVfgwv1uhipGfKSGTk5DQSIo7sDWgCb066nmcDBjs7O/WzNLE4aeLpYs0dHZ1aW0gnMZ3XwCDXsx9zm72dPsIZvnr99UKdIYtG2x/95Mdy2GGHeeFF//qoQaF/+SMgT2NQGJBum/ehDQrnbaqAvdCgMPBch6zM3ooK7eoFyKiL29e5TyN/RAeJZiGtghB1WmqKtLW1KdQxno6IntbUpaYKHcRIvdTWIzbtiaihZUhdH8CJliGdvTSjAG6A5auv7pDbbr1V2lpb1XDr1q+XS6+4UiOU3T29KoHzT3mZMW3+4H9h4Z5GFCRmGHenUEeXCYLSsbEKb5yZRVobwHO6pAFJ5jMDhAhsOwswJipI3SPXD/QjiTOiwMl+zHWeSZfQG48/9+yz8l//9QVpbmqSx7c9odqIblkGhW7x5Ao+h0HhChp/GW5tULgMRl7hWxgUrrADFnh7agSp7XPSuFFR0dLV7RFzpo6OWjxUQtDvIy0MMNGA4ggwE42jqxgwRIC6u9sTaQQew8MjpLK6WhrqG6RvYEBlZUjrpqemSGdHp9YNVlZU6PXpGRmy9fLLZf0hG7TGcHCQaSSO+DQwSHQwSCGOWcPpCEcnxsvY6Kimr1k0hQBvztxhmleIDCJm7XzfmUuss4wnlkeCpkMjm0xZo94RQCR9ThST5/M1DE53E9qVxxxzzAK959+XGxT6t38C4nQGhQHhpkUf0qBw0aYLmA+uVigk4nPscccFjJ+AQBpHgDwWqV8W0ULSrCHBIRIXF6vNGTqCrq9P6wYBJlK8gFdeXq52CpNiJs1K1BAwI2rIuDv2B7LI9RI1jI+N1d9/fcftgr04Q1x8vJx1zrly9LHH6XWDAwPatYzOIFBImlgjg2FhkpycJEUF+Vp7yDmBPpaT1k1LTZPg4CBthkFjsKfXA6hMQnHSxFPH7ZEWpq6QtDYj9pxOa54hJytLsrMzNRppa3EWMChcnN3sU1MsYFDo7tfBoNDd/uXpViMUfu2Gr8ntt90mN3ztBnnf+9/v906eKjdDRCwoOFgbSIAkpogAXQAcOn5E1OgcdlKvQF1MdJSUlpRoVJDoIIAGVDLTV2cV19Rq5M2pGyRVTMTxwQcekEceesjThRweLiefeqqcdOq7NJVMihkJGbqKgUUPqAbraDpkb9aWlerovN6+Xmlt9YBscHCIRgb5BTQ6sjJoErJiY2I9DSTTmkGokWzr6JSmpibpHxhUyOX8AG5ubrZkpmdMNqX4vTP9+IAGhX7snEA5mkFhoHhqcec0KFyc3QLpU6sNCv/7S/8td/32t+qi73z3O3LJ1q1+7S6meVRUVGqtHCBGOhbwo8uW9DCNH0QGPSPomid1BbnGGU3X2toi/YODk3OO0SgkqsfUk9aJkXBAFlI1pF1feuEFufd3v5Oe7m5NAW/ecqScec45Ehsbp1FBpG+IMrL4PveieYToXnFRgU4cIaJHTaJHVJr0tAcGObNHcLpDu4NZNJbw2eQkT00hC9Ds6KSDulP38UQ8ByUqMlIjotRLklpmP39dRF2ZhhMoy6AwUDzlx+c0KPRj5/jgaAaFPjCin2+xWqAQiPnUJz4pDz/8sDZi/PjHP5YzzjzTr71DYwhSMMATdXTM7wWMiNBp00ZMjE4socEDaRoHwACsnOwsjaaRamUUHSlWGjCYdczXmrRLt18jjtQNUo+H+PRvfvUraWluVrsUl5TIuRdcKCmpaTI+NqaRRE9QcFxBMDSEsXQRGhnMz89TfUS6gIE4Z/YwAJqWlipRkVEKg0yJcWoKE+LjFQandgbzPZplSCkT7aR5BAgFBhMSE1RUm6YTR2vRXx345JNPyiev/oRc+7nPyfve/z6FZ39fBoX+7qEAOJ9BYQA4yYsjGhR6YbwA+ehqgcKPf+xj8ugjj6pXbr/jdjn5lFP81kPAF2LUTBrp7vFEBIEigAldPmryqB0kOsd0Ef6esgDF/LxchT+0/dAc5DOIUSMoTYoY2CL6COQBg8BV175Oueeuu2Tvnj26T2pampxx9tlSumadXudJDnsWNYDajRwVJUmJCZKZni6FhQUaxeTfB06dHyltIoOkeJ00sXNO0spE+YBCZ+3b1zWhrdipaXH2ATx5bk/nsSetPLXhxG8dKCLXfPYa+eMf/qBHRPT6xq/fKGvXrvXnI4tBoV+7JzAOZ1AYGH5a7CkNChdrucD53GqAQgcIgavbf3mHX3eNAnA7d+/RqBpaf0TR6NilfQMxZ+RckKBh/BrdxiwgUDtu4+M1vetMMlGICwrSvegQ1ojj0JDCIHA10N8nD95/v+zYvl33Ye+T3nWabDnyKBkbH5/QFpwQnA4OVqFp6gmZjkKED8FropFEBgFNZw9gEJkZooI0kOwf9kxAIWrI50j/sogmelLEyOn0ahR0UgInKlJSkhCoBgY9I/kCbf3+f/9Xvn7j17Vul/Uf//kf8olP+q/otUFhoL1hfnheg0I/dIoPj2RQ6ENj+ulWbofCa6+5Vv7w+99rtO3WX/xCjj/heD/1hKjm3htvvqmTQ2gQIfLHjGCgz9EQBJyI9rH4GlqDgBbpSeCM6SakkYFDGkQ693VNpp8BOCCR3x/44x/k2X/8Q/fBNseecKIcfeyxEhrmmRACNLIn11LHyFQU5GyokSOFSwSvXUfodXnANMKjDRgfHzcZGXRmKRPhY5oK6W4W3dKeFPE+GR7ePyEpM6ZRS9Lc1BYCg9wv0Ne+zk65fpro9Y3f+LqcdNJJfvdoBoV+55LAO5BBYeD5bCEnNihciLUC81q3QyFza//93z4sN//wZr9NGdNU8dbbO7UzWGViIqN05ByQBJQh6gwA0rzhiE/TOYxwMlqCfB2JGYCRdDFC1HT0AodIt4yNe4BroL9fntr2hDz5xBOTL+sxxx8vx514kkRGRk02jbBnMI0nYaGaok6Ii9fonkb5YuNkX3fXJAzSRaxTU+JiFUCJSmqHdFDQpKwMEjPMNe7c16kgSGobYBwYGFIpG1Li3IcUN2PonEhiYP6NmvnUSPp86YtfkqqqKr3gmmuvlf/82H/61SMaFPqVOwLzMAaFgem3+Z7aoHC+lgrc69wOhXgGSRNndJq/eYru2ldee32iEzdIJ37oCLjQUK0dJCWMj+g+ZpGCpZ6QkXY0YiA/w99TavoQsOZ3GkH459GREY34EZl79qmn5Oknt00+/qYjtsgJp5wicXHxQgsEqWEkZYBPaga5d0xMtDa30JGcmIC8TN8BMAgkxsZEyz6dQNKhUU1kZxzB6aioSE1xE9lEo5DIJePnAEKkbEhFM0dZU8QpyVp/6Pb1/e99X2695Ra574H7pbS01K8e16DQr9wRmIcxKAxMv8331AaF87VU4F63GqDQH73D361de/aqaDTRP2AKACRNS5SNRg3qC53mDKJtBXm5KuzM16kbBPYYK4f+oDPyju95aviCpL+3V57c9oS88OyzCmIA4qEbD1cYTEhInEwPh4d5AFQ7ikNDNXJHpy/pXqAQmEMCh0VkEBgkskfXc0eHZ44yn9NmEL4XHj4pJ+N8jvpIihSpj3SioOxDaplnXk3LX6VqDApX01u4RM9qULhEhvWTbQ0K/cQRS3gMg8IlNO4MW5NaBegYPTc4NKgSL0TUAEKP3l+EpowdDT8Ai8ggzR1IszQ2NmpXMvAHcAFbXA+40aTB/v19vfLUtm3y4nPP6deBzA0bN8qJJ58qiUlJnvFzISETXc0RKoZNCpt0MTWDsdHR2nTC15wGEmAQgONzXT09Gn1lhSNWPdEdTNe0IyfjwOzwMKlkUfAlusnzaY0hsjLMP7blNxYwKPQbVwTuQQwKA9d38zm5QeF8rBTY1xgULo//ACxG1DG3mLo7FX8mIhgbqwCG1AuQRD0g1wJ6iFKnp6VNNpG0tLbpXOCurm6NEHINItQ0awztH1Ipl3886YFBIofA3/oNh8qJp5yiWoP8mXugSUikD1ij1g8YpcuZ9C0pXf7sSMugaxifALAGee47MbeYa6kBpDO4h4jhPo/QtLMm5AwnUsrBek9PJ3GKpqlt+Z8FDAr9zycBdyKDwoBz2YIObFC4IHMF5MUGhUvvNmCKNDHTQ2iyIDLHrGJAzNNMEixjox49QG3QSE2R7MxMTckSeatvaNBUcVd3jwwM9EtISKhGBIkMEgmkgeSZp5/SNLGKRgcFybr1h+hIOjQH2ZOu3riYaP0eyxG6pl6QLuegIISogVKPfAx1jYzHIw1N7aJzPR3BzDQGCh05mf4BjzQOi9pEUsTO6DukaWgeAQhtzd8C3/3Od+Rfr7pKwXu5lkHhclnaxfcxKHSxc0W0nok5o4jN2nKnBdwAhQ0NDRp5y83N9Ssn0QlMqpgaMuBueGRYYZBoHTAWRItHkKKgnpsUcm5ujkbraNCoqavT6Bu1e3QTA3caGRwZluHhERkc6FdZmReefcZTexgUJGvXrZOT33W6pKWnK1RSgxgdGSnDo8P0n2jEjz0AQeRjPGnjsEmIAx5JCdM0Aogq6AWHKAjyCzs7cjJjY54RdmGhHt1DmmGcr/EsgCCd07YWZgHGMDKOkVT+dddfLxdedOHCNljk1QaFizScfeyfFjAodPfbYFDobv/ydIEOhfxHy2VbLxXA8Ne/+Y0cetihK+40mjrqGxt1goin9q9HoWmU8XRxcRMj2oJU/0+jeJGRkpebq1IspIXr6xtUYga9Qmr3dLwcY+ZGR/Wf2fO5fzwtzz3zjAxNpHPL1q6TU047TTIyMhUEgc6E+DjVLmTP6Kho/TzfS0xA5HrU02kcGqL2ioig4zlE98emLKKFdDsDeH39fZNyMo6BSQkDokQXHU1CrgcGaVCxtTgLlJeXy+euuVZ27NihGzCO8Ws3fk3S0tIWt+E8P2VQOE9D2WUHt4BBobvfDoNCd/vXDVD40X//iPz1r3+VoqIieeDBPyn0rNQi6tbc0qqzhYEk7QrWRg/RSFxsXJymiSMjwrUekAidIz7N9QhP19bX6+eoHSSi51njKuFCYwowSHRwcALcSteskZPfdZrk5OZKQnyC5OZma/q2mZFz/QN6r5HhEYmNi9WoHSlnAJVopFNj6DSqOCliwDUlKUmbQpCSceRkOIkTfQRSkb1xdBOd5hHqI215bwHel9tvu13+57vfVUgnavjlr3xZLtm61fvND7KDQeGSmXb1bGxQ6G5fGxS627+BDoU/+P4P5KYf/EDLG9B9y8vLWzGHAU5E+Jw6P5ovgC4aQLR5AwicmNjhTCehiYR/+Tc2NWs38r7u7knRaUBNcXBsTIb2D8tzTz8lz/zjaa0fZJWUlsnJp50mBYWFKhFTVlqsQtV1dfXS09erKV1qFZk0EhHp6WjmXghjEx0kJRwUHDQZ4eOsRPm0yxmhaaaVTMjQcL+Y6BgPYI6OSVe3Z4oJtY0eGZpkjXba8r0Famtq5POf+7w8//zzuvkFF14gV/3bv8nGjRt9fjODQp+bdPVtaFDobp8bFLrbv4EMhUQHiRICO3fdfbdsOXLLijgL6RjqBhF2ZhE9I+qHVAyRN8SZwyPCtTEDGMxITxemkXDu6ppa2b1nr0q8kBIG2kJDQnXKB+PoiAw++/TT8sxTT01K1BSVlMi7zjhTioqKJSszU0pLijQSueO11xUKKU9ExiYqCuHpWO1m5mx0CXNPYFCXp4xR9QmBweiYaBnoH1ChaUdOhosYOceZ0D6k4cT5jMJgcrJ+3tbSWoD3gjrDb37jm/ofDaeffrr8/NZbfH5Tg0Kfm3T1bWhQ6G6fGxS627+BCoVvvvGGXHH5FQpSzJF9z3ves+yOouu3vqFRR8yxtBt46J/SME4DBylbunoZBUeqmChcZVW1VFRVab0g2oPjY+MSGuYZaTc+NioDg0OaJv4HMDgBm4VFxXLamWcK6WJ0CxGyJjr38o4dCmukcYE3RK+ZRKJgOjgkUdFRnvRxbOzkuDvOS5oXUEQ0m4jgVDkZ0sakkOFGIMSRpyHK6GgSOpHMZTf8Kr4hPrrj9jvkggvOl9KyMp9bwqDQ5yZdfRsaFLrb5waF7vZvIEIhEzTefe550tLSIh/4wAfk/11/3bI6CfiiCaSpucWjNUiKd3xcu4V7lwtKyQAAIABJREFUensmxaSTEhMUrEjtEm2jvo+IYk19vdYDUiPITGJ0AENCPeLTfJ0Zuc889aT09fbq3nn5BXLGOWfL+vWHSHZWluTl5mgTyYsvvyKtrS0yNk5UMVjvRWQQGOwfGJToqEjP6LrgkAkFgQTdD0iloYV6RbqIp8rJAJToF3I2vud0EsfGxEpKSpJGBkkz23KnBQwK3enXZX0qg8JlNfey38ygcNlNvuw3DLTu46/d8DW5/bbb5PgTjtdu4+VcpFbRDCQlyyIdPDIyLIhKk6IFDum6BZ5IySLvQjq5sbFJ07I0DABxLNLKoWFhGu0cGBiUl55/Tv7x1JPSOyEDk1dQIGecdY4cvulwFbHOy8uVuJgYnZPMvGOADUkbIoBAJ7WMgKfuGxqqTSyeZpZQ7Q6mu5mvcT/qHx2gpS4Q7UGaT0hXO5NKOCPNDWgMoqdoy/0WMCh0v4+X/AkNCpfcxCt6A4PCFTX/stw80KAQo9Bg8q9X/aumSpdjUTeIZiDRQBYAFRsTLXUNjTqdZHRkVOf3IjSclJAoYeFhCldAGgCGXiERNmJs6AQGEb3r79fo4MsvvaRTSHommjpy8/PlzLPOkc1bjpCc7CwpzM9XsHtr5y49gzOpJDIySohG6li7/oGJiSjhkzWMwKFHsDpG9QZpdHFG5/EM1DhGR9MpTONIr+zfPzRpSqCWX0QUba0eCxgUrh5fL9mTGhQumWn9YmODQr9ww5IeIhChcEkNMmXz6XWDgB2w1N7ZKZWVVdp8wSQQwCs5xTMXmNQrEUHq/Dxzh4NldMwz4YPaQRWeHtovO155RZ5+8gnpnmjeQFLmrHPPk6OPOUZrBosK8lQzcM/ecqmurdUIH/ensQPdQBCTWj9EpkNDPTOF0Q0EIIFlfkesmgglDSjUGXINUUG6jvcP7dfvOYvvEXFMIsJpncTL9Yr51X0MCv3KHYF5GIPCwPTbfE9tUDhfSwXudQaF7/QdqVUigDSSOGlWYDA4SOTVN96Snt5e/ToSM0AUoAX40b1LVJBZxMDhyOiITh5BVgYpF1LNr+3YIf/Ytk327fMAWVZOjpxz7nlywkknab1gXk62RgPLK6uktrZO+iZGyBH5i42N067kgcEBrQkkTeyJ+EVrMwuRQWoIkcFxOoj5M9HJ7OxsTTl3dOxTIWpnAZAKg4mJGgG1tXotYFC4en3vsyc3KPSZKf1yI4NCv3SLTw9lUPhPcwJ61AfSSOJM6AD4aOCglq+1tU1hkKgfen4Z6Rka+QPQ9jMScmhQO32Bsv1Dw3od15PifeP11+TpbU9I50S3clZ2tpx97nly2umnS35ermRlZWp6lwgk01AAT8oPVdImPGyiHnBIu5WBUWoXo6OjJCw8XMJDQ/Va7ussoonUAhK9pAaRqKPzTMAk509OTJLYWBOb9ulfqADezKAwgJ3nL0c3KPQXTyzNOQwKl8au/rSrQaGne7i1rU07ikn5soAuZFt2792rotTAGAsQy8nKVkije5g0LPWDRAgZJ6efVxgc1xFwr+14Rba/+KLU19Xq59MzMuTs894t5737PCnKz5e0tFSVhKmqrpHGpiZN9QKRpH+DQ0IVAIk8ImVDNzGQSnqXukWihlzrdAR7RtglKAySwu7o3KdjDKk5JH3M8yQnkiJO1PPbMgtMtYBBob0PXlvAoNBrE/r1BgaFfu0enxxuNUMhMIjOIDDmdBQz7xe9P77W0NQkw/v3K9wBZ/n5eZIYn6DgR1dxZ1eX6ggyyo4oHPsh+Mw84pdeeF5efP65SWkZDwyeJxdeeJEUFxUovFF3iIB1S0urRgaHR0Y0ske6F5mZkYkoY3hYuM4rBgojwoFR0TnFLOAOCGQ/HUvX0akwSIrZWexZWFCgUja2zAIHs4BBob0bXlvAoNBrE/r1BgaFfu0enxzOX6Hwu9/5jlz9iU8o6CzF6ujoVOjjHffUDQbpZJD29g6N3BH1cwSo09NSJS8nR2VniOQBczq5BBiciCASraNO8Ll//ENe3b59MuJYUFQkp51xhgcGC/NVQmbfvi6pqa2dmE/cr0AaHOKp59OzjAdp/R+ASoQvHC3D4GAdT0fql7PSeexEBemKpmmEX04NJOPtiAhyTV9fr6SlpS2FGW1PF1nAoNBFzlypRzEoXCnLL899DQqXx84reRd/hMJPffJT8uCf/iTvfve75aYf3uxT8yAR09DYpPV7HiD0iEjT3QvwOZCoEbiEBMnISFcAJAXb1dWleoBEBakjZBHVa25q0nF0e3fv0n1YGzdtltPPPFNOfdepUlJYKFFRkSpPg6wMtYmkd7UJZZwaRZHhEdLAnlQ2QMf1npnJwZou9sjgxExGBTmfBwT3HagtqI0jnhnGgCqQ2N7eblDo07fInZsZFLrTr8v6VAaFy2ruZb+ZQeGym3zZb+hvUPiTH/9EvvPtb2tE7b4H7peioiKf2IToX11dvYIZUUBq9GjiIPUL9I2OjsjY6JhCGBM8iMohJwO8If1CNI9rkJVBcBBh6L27dqusTE11tZ6Rpo8jjzpazjz7bDnqyC1SUlKsc4iBN6aZtLW1615EAR2w1BrEINLFQfp5QJBfCoWRkZMyMgAqTSEIXTsw6GgLhoWGeRpHkhK1bnDqMij0yeuzKjYxKFwVbl7ahzQoXFr7rvTuBoUr7YGlv78/QeGTTz4pV33oX/8/e+cBXld1Zf+tLluSLVmy3Au404uB0CEJmZSZTCYEAilkUkgomZlUyJCQmcmkkEx6J6RMJskMqSRAAvlDKKEZg+nYxgbjinGRZBWrWO3//fY++76rZ0mWZOnpSb4H/D3p6ZZzz7ll3bX3WlsZrp/9/GfyilNPPegBINT7/AsbZE99g7KAMHvk6JG/R75gBx6CAD2CsqGEm/7W3W3CkX3tyiTCKLoBNeKR+/96r9TW1Oh6kyZPltPOOEPOeeUrZemSJbJk0UIN82JrAytJ3iLgkkZ9ZPa7LzCDCgYLCrW8HKXqKE/nfoKeK6ih6fp6LT0X9xaEOcQSBzBoYeX9WwIKD/oUOmQ2kIDCQ2aqR+5AE1A4cmObDVtOQGE2zMLI9iFbQOHz69fLP/zDP0jz3ma59tPXyj+++91DPnBYuB07d8nGzZs1f48QLeFXwBcgDKCEFyCMHyFcfqb8HAyeCjw6O4OVDKHdLv0ORm/liodkxQP3R5VBps+YIWeec46cceZZWn1k2ZLFyiDu3LVLlcz19Q3KDJIPyCehZbZNuJjvUBhPnDBRJpdP0hBxebnlAPIPGxqOQ1nBmLcg7KWZTJerifWBWgIKDzRCyd99BBJQmJwLBz0CCSg86CHM6g0koDCrp2dYOpcNoJBcvTe87vWyfft2edOb3iRf+dpXB31shIMbGhrUWobycy3B9BkwOGHCRGXSKDNHfd+9e7F96VImEEsXbwA6QKJ7EfJ7Y329PHDfvfLYo4+az19OjixatEjOPPeVctJJJ0nllApZGMLEu2pq5OWXd0hTU5PsbW5R0Ne0t1nL43UBBgW2MVfDwyiBJ00qi0AgrCBG1LS4cMS9BQklkysIIByM+CYBhYM+lQ7ZFRJQeMhO/fAdeAIKh28ss3FLCSjMxlkZ3j6NNigE9Lzt4otl1aOr5MTlJ8r//t//9RkKTT9yB4LkC9bU1sme+j2R0IM8O0AXVjIAORi3xqa9Cs4Qi8T9/QB/bMvBILmG+Ared889snbNahV/YAdzzLHHybmvfpUsW7pMykpLZf78uWpfAxClD6iTEbCwPYAdv5sgxcBgWWmJlsmDCZwyxSqhxG1iPFcQkOyNZSxfsGJIE5+AwiEN2yG5UgIKD8lpH96DTkDh8I5ntm0tAYXZNiPD35/RBoWbN22Wt154obJfv//D76X8AOAHwUdDY6MqbusbGgWxBR5/5Ozl5eVrGJbSbQhFYOxYBsBGqTmAIOFb2ENYQ8AioI0QMbFk/PzWrV0j9959d2Q2PWHiRDnplFPk3Fe+Sn0KJ5aUyIxp03T7u2tqFYQCAPEFBIA1t5iK2VXF7AuPwenTpsnUqspIPew5gADUdG9BlMWuIHb2cKgzn4DCoY7cobdeAgoPvTkf9iNOQOGwD2lWbTABhVk1HSPSmdEGhRzU7t27ZU9dnSxctKjXYwTwNTQ2RWAQ5g6AB/ja175PigqLpLi4SMEg4KyxoUlZOq9RbAyg2cfwAyXfxLQlJi7JEXl81aNy3913awUQ2pQplXLqGWfImWefLdOqp2pdYUQdebmIPhp0/4ShCRMjWoEhBCC65yFsYcXkSbJw4QIFeFqJZEJxdHyNjU37eQuiuCY8zPKsPxwtAYXDMYqHxjYSUHhozPOIHmUCCkd0eEd94wko7DkFHnKE/RlLDWDw2GOPycMPPyynnHKKLF++POp+NoDC3sYSls+BIODLm4pE2ttV+EGYF4YRZTCgDDFHW1ur5vFhLwMTqILibv43IOlAMC83T2sFIxzBY9D9BefMm6fCkZNPfYVUlJfLxAkTzC8wiEVYXwFnY5MKVBQUtrcrE5mDwXRenoaGly1doswg5fLifU/3FmS7zgrGlx2u8ysBhcM1kuN/OwkoHP9zPOJHmIDCER/iUd1BAgpTww879apXvUre9ra3yfve975RnZfB7vzWW2+V73znO9rvhQsXyrHHHpt1oBDwYmFhYwQdpHlHCaPua+/QMDGhW85NQsGYSnd0tOvv1B/u7OxWRhAGkDlzVlHBoFi5uro9tRoifmLVKmX2AHPLjjhCzn7lq+SII45QVS8WMRpmzqHKiG0H5hEW0nwL90kHvoVBSUw4uKpyihx51BEyc9q0Hkxfb96CMI+mIq5QL8ORagkoHKmRHX/bTUDh+JvTjB9RAgozPuQZ3WECClPD/eijj8oHP/hBmThxovzlL3+JPO0yOiFD3NnHP/5xOeGEE+Tiiy/ebwujyRTCsAEAYQQbGxqlvaM96l9ubp6ybKWlE6W1tU1Np2EDAX7uHcj6ra37NHyLnYyGXAMrCBjSsDH+gngTFhbKxg0b5N6775Ln163T/WAWfcKJy+XsV54r8+cfJpPKSnUbWsE4J0dtY7TO8d5mqdtTH0yvTZ0MAYnRNYBuCmBw6RKZNXNm1H9YSbwFscTh0xu2MwoGy8uHOJuDWy0BhYMbr0N56QQUHsqzP0zHnoDCYRrILN1MAgpTE3PNNdcoi/SLX/xCPve5zynI+v3vfy/333+/fPnLX44WvPrqqzVE+/d///fyve99T37+85/r3971rnfJ5Zdfrj//y7/8i3ryff/735dVq1bJ2rVr5Ve/+pX85Cc/kZ07d8orX/lK+ehHPyqzZs3SkOe3vvUt+dOf/qR/mzJliqpzf/3rXytw+fd//3e56667pLq6Wj75yU/K2Wef3eNs+rd/+zf53//9X610wbosG2+ZBoWAOkQiDQ0GBk3kYQ3gBhAsKyvVkm6EWrdue0nZw+aWZlUIg/qwjUEg4kydl4fDTxAQ1NnVqeMG0wfIW/30U8oMUo6OVlpWJq847TQ565xztYwduXxmGSMa/mUdzn36B6gDrBKOdrAIU6kG0+WTZcnChTJ71kzdF41jqwtgUKuVhONyVpBwdCZbAgozOdpje1+DBoXmBo/hZsGAjhwvp/Xr1w9o2WSh4R0Bxr639u53v1t4uA1XS0DhcI1kdm4nAYU2L+S3HX/88fLggw8qENyyZYt85jOfkZdfflnOPPNMzdUDcAGw8K675557ZPPmzQrSvvrVr6q/HaHb3/72t7JgwQK56KKLFAh+4hOfUBA3Y8YM3TZghLJubBsAesUVV8hDDz0kn//85xVc1tXVyXnnnSe33XabhoEBi6tXr5arrrpKwSXg9IEHHugRuoRde//73y9vfvOb5TWveY0CoEyDQnLwAIEAJn6ON8KoAEEHg4CYjZs2Kxj0HEFTCBPCFQWCNAsLd2l4F0NqABvjrCxeTo7+vGrlw/Lg/fdLU2OjrlM9bZqccdbZCgjJ+wOgof5lw5ab2GU1jhswnW7VsDSNsHNefp5WQikqCjWRq6vlsPnzdD2YTOxwAJCUzPNGhZIp5RYizssbnTzUBBRm5701G3s1YFDIzeuzn/2sPPPMM3ocf/M3f6Nvp1zM/bUEFI7etPOWzE3z8ccfl4985CNy9913282NkMgwqdrYXgIKR2+OM7HnBBTaKP/ud78T8vJ+/OMfy9atW+Xcc8+Vp556Su+B//iP/yivf/3r5cILL1TQd9NNNymA++IXv6jXGjmItP/8z/9UdvHSSy9VULh48WIFf+kNj7qbb75ZQ9T//d//Ld/+9rcVfHIPpsEifulLX1KxyN/93d/JP//zP8uRRx6pf6MfrHPcccf12Ox73vMe7d9rX/va/fY3Ekwh1UEIB1to2PID77jjTjn8sMNkwcIF6vEHYMJH0C1XYAU3b9kqO3bu1Hw9rGfIGcTfj9Aw9zMY0o5gLq2i4WAtA7Az1a/I3sZGeeiB+2XVI49o6Je2YNEiOevcc+X4447X/ZIvCPgjBoyIhJw/AChqZrYFe+n3Sv4OMwiLCds6tbJSZs2aqcdASNlCxKZYphH2dgUxjOdotwQUjvYMjJ39DxgUcvPjzZgbDm+d733ve/UGw5tnfy0BhaN/MqA4JFR13333aWe42Z5//vkamuKBxBxdd911+t0dd9wRAUZCTqeffroyC1QJ6CtEFQeFTzzxhFx//fXKbHDjhVF+61vfKh/4wAdGfyCSHgxpBBJQaMMGiIOJq6ys1N9ramrkK1/5irzxjW9U5vA3v/mNAkEAIt9xb3zd616nzB4skTcAHfl9bA+gxvXlDfD3xz/+UX8F/EyePFm3+cgjjyiQhHXEuoVQMEwk1+XJJ5+szKK/6PEyyLXNi3u8ZQIUEtLVsHD454CMfjz+2ONy002/k/q6Ovm/X94oc2bP1u7ByNXW1sm27dt1Xe5PLa1tCgABg2r6DEuXZ2FhQCJIDmYQQMfyrgjftnWrqojXrn7WzKbz8uTo446TV5/3Glm4eJGUQGLk5GgZPXIM+U/BYCuK5TbpJDStrCMAMF9D2DCT7MprDFPKDlNszxXEDscbDKwaTZdTom7khCODvZATUDjYETt0lx8wKEwfom9+85t6AXOTSkBhdp9A6aCQm99RRx2lzMKHP/xh/ZmbxmmnnabhLH+4XHnllfLqV79a8576C1HFQSHlqcibesMb3qDhLh6I3/jGN7J7gJLe9TsCCSgUefHFFxW83XLLLVHqzJ///GdZsWKF/M///I/eC2EA//CHP2geIeARvzyAHyCQ0G1642+XXXaZnHPOOfonrlOAG4w+IBIwePvtt+snoIeXtnnz5mmomm0SqoZ9O/roo+WXv/yl7r+/NlKgkD6oSCQAQWfr6IvnB7644QW54rLLFXh9/Kqr5OK3v01DybtrahQQ7m3eK21tJhZRNhChB2As15TCeApaqTc8Brss3w/lb1j+uTVr1FZm65YtOgTFxRPklFNPlfNe+1qZM3uWzplbx5j4pFPa2tqDepjcww6tSkJqVPGEIikrLdNlWBYwyFxWVVbqfgGDcXuc4iLqFVOreJKyiNnYElCYjbOSnX0aEijkogUoABrIbUlAYXZOrveqL1D4ta99Tf72b/9WFwPY9QcK+wtROSjkhn/MMcfIvffeKzNnzlTGgzAWyfBJG7sjkIBCka9//evK0Hn4ltnkhQeWDtHGnDlzNEVj06ZNMnfuXOHaov3whz9U8Qgv0UuWLNFoC/VrEYSkg0IAJSITws+wkABJmCdAIXnZF1xwQSQW4fryvG7yFFFDf+pTn1IWk2Xnz5+v+4m34QSFgCL3DyTXMt7I0dOwMGKRSWWy8cUX5U1v/HtV+f7dG98o519wQahE0iB797ZIR2e7dLSbIAQlL0phwCT5e+0K/Agbm98g7CCWNIC4ttZWeeH59XLn7X+W+noL3VIJ5cyzzpa/ef3rtR4xIBLACQBV8QnVTHR73QpAYQABeiiMAXQAQFc/E9ImNaC0tEQZy/r6BjM7FFsHRtDA4OSsv7gTUJj1U5Q1HRwSKCQ8SCiSB76X6eGInnzyyf0O7C1veYs8++yzWXPAh2JHCOnywHLFIQ95WIW//vWvUSiMBx7J7qQJOFP4T//0T8oUnnXWWXLGGWfogyYeovrQhz6kLwXkP/EmTf4NDx4eTORb/fSnP1V2gzSDpI3dESAEyDmTLk4Yu0c0uJ7zQOXagPFOZ+O4rgB7pEdwT4T5++53vxupfxk38gph8rzdcMMN+gL2jne8Q0PCrhQGaKFMhq2nEYbGAoccxnXr1umL+OwQcgWQYo1zySWXyPbt2zVig9CFBoNITmNVVVWPAwVkAix7e5EH2CGW6EtAGPnzwQg2Ne3nH8i5oTmCpaUycWIqz/zlHTvk6quuls6ubs0jfNWrz1PBjuUKdqjZM/l33DsAhYVFBZKXYyxgezt5fZYDTRSZPEJCx6iHH334YXn6ySeifMEZM2fKeX/zWnnVq1+tFUPIFSS0juADf8GukB9oLCFh5dygSs7VfMaSiYBBwsA5Ib8R0UmxhpfjFjkAXeoU42EYf/YN7ozK/NLMH+NBOkLSxu8IDEfKwqBBIewP+Wfk0HhujQ/xxz72sf1Gm7fflStXjt9ZGANHBtBDbUySPI0wCiCPJHbe6Gk8ZMhBAig6w8Dv5CJi1kvICtYDJjC9sT0eJty8WZ8EeBhIHnyEpsda5YcxMKUZ7aJ7vY2lh2BGB2gAO7NybE0KrA8k8mI5mD+/bliXXG7ApYtHeNEmUkOoWUu0iShQA8CzD/9uAF3TRQjDKlMXq9ICANMSbnubVS1MvqA3QJUyawCqkolR/hznCpVEWA8LGZ4TtbW1MnPWbFm6bGkwgDZgBitIPzmvyNEDuNAPKowoEJQcBXMwh3w+vmqVPP7oI1GImL4ce/zxcvY558pJJ5+kIefdtbXa131t+5TTw57GxwLhC2IRkCbHCQMIE2jq4hytjMIx0h/myNejjjK5hfxDcDIWmzKjVH/JojzHsTiO2d7neO7yUPs6KFBIWBD/LRgg3o4H0hKhyUBGaWSX6St87HlPvndypsgxBAySxA77AcCDoegvRBXPKQREwmbASMA8YLORtLE9Akn4eHTnD1CIYAUQCAOPCpkozYYNG+TGG28cls65+hggFfcPJK/Om+cHum2MvyQA5FRYgtI4mE+TH4g4Ztfu3QoeiTJYrTmRgrx8yxUML5IAsn372rRsHeFhrxzCvnft3CkrV6wQchL5mcaD77Qzz5TzXvM3mmPZ0tIsO3ftVgazU0PC+BLmSn5BgZlW5wAC8zRHkGOALSPEzbiqsbWItLW2SW5enpSWGBgvKCiU8vJJGhoeibJzwzJpg9hIEj4exGAd4osOGBQSxgAY/OhHP4qsDxi79LyV9PFMQOHon2G9hY9h8NJBIRYY5E7xZs9NfOrUqSoYQTzy0ksvqZ8aqmIaLDFJ9yzjoJCHA2wxbCE5U5js8klOFQ7+SRubI5CAwtGfN9h+cnO5llEaE8bm2uT6O9hGiPWll7YrKEsvKzdxwkRlyLCNiYMjFLsKHin51tioXoEwfJwrsG2wUjt27JSdO3fIrFmz9TmhrCAMnJpJ5xoYa2tTw2jwIrl+sHmsS2iYEDFqYm9Lli2TV77q1XLKaadK6YSJWt2kprZWK4yYUjlHX0Stogm/WwYggAgQyD2IyiMsh6cgEQ7WBSgS9oZFjOcJjqcIRwIKD/YqOXTWHzAoJPcF9ii9Ecboj5JOQOHYO5m4yXtYOb331BzlZuo5hPzdQSEJ8igyqdDgLALnDerKt7/97WNvIJIe6wgkoHD8nQhWScSMpPHmAwzm5xcoMIpEImWlkX8gI+A1iVkHIAkQ49yAFQQUIgzW8C/WLkHQASzLy88P4WBTI2sVko52E3wIP3cqo7dt6xZ5dOVKefbpp/Qeo6zglCly0imvkFefd54CYMAkQBAvQcLb7ltIiBexiLoUdltpOzoEoKWUHKwk+Yn0nWMlZxGgWFpmFjL+D+/C8dgSUDgeZ3VkjmnAoHCou09A4VBHbuys56CQElykFqC8JCcKo3NMdREmUfIraWNzBBJQmPl5A+zgZUguMMKRg20Ar7h/oIMutuvq28rKKVI5ZYqybTQYO/ICnQ1kHcAFIJBzQsvB5edp7h8gixCwAUTAmtnJwNYV5BeGPEqqj3QKvn6Ui4NRpGzdU48/LqseWRmFhwGRy444Uk49/TQ57rjjpai4SIUp5FoCYOkDYWbUzOT40X9yDmEcu7pFwSFiEJhNrGna9rXKnjqqkxiQBUAiwplaVZnVNjIHO+fx9RNQOJyjOb63lYDC8T2/GTk6B4XccKnzeuedd+qNmlJfCFr4l7SxOwIJKByduUNYsmzZMjXCHkrzur0OBgFk3goLi2QSYeFgG0MJOEQX+AECBFmHT8AW6wH21BMwmGoXFRZo7h/7aNrbJC0tbarSVXmIVkzKFfahVUAKCqSltUVa8SHc1655fxs2vCCPPfqIrF29WrdPmzZ9upx40sly4kknaXpKQUG+hnlhJdWcmoVychQIojDOy8tX4Krrd3dLYVGhlE8u179Z2blW2V1TG7GOqKLnzJot1dVVY8JGZihz3tc6CSgcztEc39tKQOH4nt+MHF1S5i4jwzxqO0lA4egM/f333695u4DDgTaqTbl/IMAu3mDvAYIeHuZvajXT2CTbX35ZcwqdQSQ0q2xglygwBNgRWrVUoW6pqa0Lli8tGg6GuTOBRoEycR6G3dvSrBVDAJR7auvk8cdWyROPrZI9dXXaNWxfjjrmGDnx5JNlzty5ZouTny8tra1RX1iObbNds0XqVrBI3wE7qJ8xmwaoFhYVacUtwKCDTcLH8+fOkWnTp+m2D8WWgMJDcdaHdswJKBzauB2Sa73wwgtaRxnvyXhLQOH4Ph0SUDg68wvooToKSuP+QsiEVcns1ssdAAAgAElEQVT3q29oVEAUbw4AAYOAQhrsmlcgARASzoVVg/lTgJeXYwbSgMCCAhWJALzIJ9720natQOLhY8AalUCKi2HvJsgEQr1sv6FRlyHsu2b1s/L4qkflhfXrFcjR5s6bL8cvXy5HH3usij9g/bCowYsQY2oYQZhBQsnY3pDDrOXv2lq1b2wHSxnMplENF+YXqPqYcQAM0m+EJQsOO0yqqg4+/D46Z8Dw7TUBhcM3luN9SwkoHO8zPIzHh8UENVe9WoNvOgGFwzjIWbipBBSO3qT0FUJ2oQifhGa9kbZhljGmFnbGDjPnxibEJRYadk9AqxvcpUCusLBAxRdsAzNnFMeFBYWyedsW2bRpi/oPqlI411hBZe5KSqRIRR456g/IMlQhQXm86pGHNV/QS8KVlJbKcccfLyeefIpUVlVZOFhZwDxl/wClWncYxlHrPk8SSshZHmGn5iCqP+JE80XEcoZlW1FCNzXpMQFOYQYXHDZfgWTSbAQSUJicCQMdgQQUDnSkkuV0BGAJqYMc9x9MQOH4PjkSUDh68+sh5M/8539KU6gmAgCKC0VgALFUgTnjE1CnFSxCXiBsICILgAHrwd7B1wHKYAOLCoukra1Vq3TASPJZ31Avz65eK7tqajQPUI2gqThSWKAh3JIJE9RhYMeOHbJx4yaZM3eOgrennnhCWcEtmzbpoJFfuHDRYjlh+Umy9Mgj9HdnC1nffAm71FtQ8w8LCxWMkiOIeMVL07GsKozz8iN/Q0LSsKSUwwM8VpRPllmzZh5y+YIDOTsTUDiQUUqW0Wu226/QERqPRH08QgM7SpuFJaTOazyEnIDCUZqMDO02AYUZGujYbrgtY7sCsPvA+y+Vj338KikLzBfVP7BSKSN8WlqqYIkG2IMNVMVwY6OGiQGBVjKuQ0Egil3CtYg4aBhLwyja3wpkw4aNsvWll6Sxaa/VGxYqjuRJWUmplJaVaOURtou/H+HkDS++KHvqauW51WtkzbPPaMiYRg3i4044UU465WSZNGmy2sfQAIFY36BKBqgoMMyF3SxVcAeghfkzu5kuE6tQmzgvT8PLhLJhIs3omt+LlDmcMWO6TKmg1nHSehuBBBQm58VARyABhQMdqWQ5HYHeQsgJKBzfJ0cCCjMzv4wzLCCADFaQXD/aL2+8URYtWqil7rzGsBsru7BE1cIwiAEIelgY0AUIhIEj9AqoIuRr+XilGpbdsHGzrFu/Xlk31McK3nJzlX2j+kdhQb6KTaj6AWMIYN2xc5eseOB+NZn2SiMAt6VHHKEK4sVLl0YhagAneX9Yxah6OYA8+oSSmH2xX7OyMdsaA4uYXOdFwhVYRgAujZxB1p85fbpMmVIx6LJ+mZnR7NlLAgqzZy6yvScJKMz2GcrC/qWHkBNQmIWTNIxdSkDhMA5mbFOq/NWKIE0KyMjJ8wYoIhTMv6efeVr+fPvtqkLm4e7rwAayHgwhAJJPgBNgCSBIPqFvx0Egtixt7e3y0raX5MWNm+TlnTstnNxtIVwNDwfQSI6fgUsrD4cY5aknn5RHVj4sz61erYpi2tTqagWCJyxfLuXlk2Vfe0dUSxlAaBY1eZoDCCDUWscF1DvOV5uazq5OtanR2ss5eRrXpp9UUzE1c5Eyh85C8t2M6dNkalXVyEzMONxqAgrH4aSO0CEloHCEBnY8bzY9hJyAwvE820lFk+GcXcKu8dxAQrHevKScgsGyUgVJNMAQL2L/+dnPaYm4vXubLTew3cLCDgLJDwRoEQ6GUXRwByjDvPql7dtly7aXtGRlc0trCA9jQJ2vzBvrANbYJkAQIAcA27Ztqzxw333y+KpVUldbq30iDA0beNrpZ8iixYsV+GkOoApRrN+as4ggJD/fahGTD4i/oVY06VBfQ4Anx8n6qJcRugBmEcoUFxUKAhl8CmlsZ/q0aTKt+uBL+w3nnI6FbSWgcCzMUnb0MQGF2TEPY6oX6SHkBBSOqekbdGcTpnDQQxatwMOY3EALCzdFSlwWAHQ5AOQTUOQNIGSm001qAfOrX96o4q4jjzpaQZeGhFUkUqjgDxDlINBLTAIEd+zcKdtf3iFbt21TJtLZPQAauYITUPIWFEp7O75/qIpzNG8QULhixUPyyMMr5Pl1WMlYWHnmrFmycPESmX/4Alm6bKmFfjG1DrWHVcCSIypeoR+APYAqPzuIpQ98D2pE5QwQJDcQUDp5UpmOy5499TpeDganVVdL9dSqCCgPfUYOzTUTUHhozvtQjjoBhUMZtWSdHirkBBSO7xMiAYWDm1/CrPHcQBgxbwC/OBAEANF4aLtdTN2ePWoM3UZYeJ9VEtm08UV56skn5N3veV8Qh1hombCwl6VjOwDB3bU18vL2HQoG99TXKxgDtKHchbED9FE6TmsFd3WFPL4uBZibN2+SVY8+qtVG3GC6eMIEOXH5SXLMccfJnvoGBXCIzQCUVs+O/nebWEVz/QqUJ4QlBEx6NRTyBhGaMAYAWCqPwGpiHQMYJB+SusYAQhrbml5dLVVVlQkYHNwpuN/SCSg8yAE8hFZPQOEhNNnDeajxEHICCodzZLNvWwko7H9O4nl+5Ph5uJO1UNYSCvb8QHLlvFG1g+Uxna6pqVFLF80P3LdPQZCxgUWaU1c+ebJ85MMf0jKSs2fP7tEhgCBAEhC4c9cuqavbI61trRYCzjXlrrKL5Bjyc05OVO0D4FZbWysrHnpQnnzsMXlp27Zo24cvXCinn3Gm5gpquLe9Q3bt2qmgtGJKhVnVBGEIwBQwyPHiWdi2j7xCAC2qYytNVzapVPMEyTsEBAIGWW/37hrZtXuXgkca25lePU3BoDKKSTvoEUhA4UEP4SGzgQQUHjJTPbwHGg8hJ6BweMc227aWgML9Z4TSbbCBgDo+PSzLkih842ygh3MBabbOXi3Dhheg+wby0CbMCggEDFZUlEv55EkhN5D8whwVmngtZMAWbOL2HTtk167dygiSf6f1h7F9gYEMoVsFhvl5qvClGggMHKrjNWvWykMP3CfPPvVUdICYSgMCTz/zTCkpKZX2jg7NE2QdwrxsY9++NgWIhIrJReRv+QX50tlueYL0TY8Hz0ENa0+UyimV6j8IGIQpBAACYAHDrnjGWqa6eqqaTydgcHjvAgkoHN7xHM9bS0DheJ7dET42VyHz0KOAvSfGj/Buk81neAQSUCjKrKlVTACB8XJynPduFQMrCLjxBgAkl6+urk5q9+xRBS9soOfVuV0M68OM4deHVYz7CMan+t57/yo33/wHufT9lymgIty8t3mv7GvbJ93SrawgQDA3x/IVCRdTKaSTknWIPfLzZNUjj8jjjz+m6mEXuQBijzn+eFl+8skyb/5hKgRBEUyoF2avqLhQwaSDX/ZFCJowsiqU29sVOJo4JV9L4mGATQ4gljaAQfdSRDFN3+vrG/TQAH8wh9VTp2pIOWkjMwIJKByZcR2PW01A4Xic1Qwdk4eQzz777AQUZmjMR2M3hyooxJzZ7F9MKKI1eUPDww8AqGCwrFRZPhoMYtPeJqmvb5TaujoVlrhdDH+3nLtCZROnVk5RQFRWWqYAq7fmjODOXbsVTF33+c/JRW9/h9YEtvCwKXdpMHdq8hxyBd2W5tFHHpEnVj0mq1c/q8bP3o+lRx4pRx9zjBx1zLEK6kgPhJEkpMs/8hXVOxHPxH0GPAGD5CV2dMI6mregK4cBgphIVygQnBQdE4CEsdi5c5cQMqfBZFZVVSlwZEySNrIjkIDCkR3f8bT1BBSOp9nM8LF4CPmaa65JQGGGxz6TuztUQKGHdwFBgEBAoTeATzwkTF4dDbAEE8g6NbV10tDYoLl22LOYuMNKt5EnV1FeIVWVU5QN9PV7m0cHYrt218jumhrNUaQvhFzvvutOqZ5WLUuXHhGMpBFvwArmCqWDYeRgGZ956il59JGVsvqZVJUR+rFoyVI56phj1GQagAeU5NislnGRTJ5crkbTHR3tITexzQQp3d3KHGqoF/SoANdK0s2ZPUsqtTwetZZT4BYmEjDLMXh4nf7BCmI4nUQWMncVJ6Awc2M91veUgMKxPoOj3H9CyP/xH/+huU7JTX6UJ2OEdj+eQSF5ePHcQIChNwCOC0SUDSwwq5YIBNbUSV19XSQOAQRqfeDABrIOBsvYxQAE+7s+3JB61+7dyqoBALVEXRtiDVMvE6pFhbx2zbPyqte8ToGglnqbUKwWMOueWyMPPfCAPPP009IWGDny+hYtXqJAcMmyZQoEc3INBMLWcYzk/XFciGAQuzTUN8i+4CGoYe4Q5nXwWFJaInNmzZKZM6bLpDLEIoU9zjzY0R27dqmK2KuoTp5MOHmq7itpmR+BBBRmfszH6h4TUDhWZy5L+k0IuaKiQi655JIEFGbJnAx3N8YTKATkxHMD42wgKtm4UpjwKY28QIQcNTW1+ql5gTHTaWMCC7UWMYwZ7BkhYbNm6b3BosEu1jc0yK6aGjW0thrFlm8ISCMXEA9ArfgRwCp5g//3i/+Rt7/jXVI9vVpeWLde7vvrvfLkE09Ia2A2AYILFy+Wo446RhYvWxoBQULcMJcOdp3BBDAARplnwtWEuzs7uyKLGY4Accj06dNkwWGHKSPIuvEG+EMBTYjY1dcwjOQaAwbTgeNwn6PJ9vofgQQUJmfIQEcgI6Dwrrvv1psKtgquxBtoB5PlsnsECCH/9Kc/lW9+85sJKMzuqRpy78Y6KASkqEBEw8J7VXnrzcCc5QXyye/kBRLyVM+8+gZBVBJnEGHbAHyAP0AgeYFaDSTkFfY10GZITb5hvaqPAZcAQbZNeJawLBVPHBgi+ACZKauXn6/q34rJ5fJ///sztZFZu3pNFOKGxQQIHnHUUbL0iCO1eoiVvCMHME+NrmH16COgkPxIWEHA3576PdLa0qql5Mxsu0nHwQBdlSw4bL5UV1crA5reWAf1M6DShSsAwOqqqVJZVamh56SN/ggkoHD052Cs9CAjoPDGX/06Gg9yabBamDxpspqXJm3sj8D555+voHDWrFlj/2CSI9hvBMYaKDQ20EFgk4KveIsrhQGCsIXk75ETCGAjPOxhT9YDVJELB/ibUlGh+XDcx8ix669pjmLIT8Q7cA+G1G1tGhK2CiHmFwhAQ4ABqFITaIp9YCuTb0reyooK2fziRrn77rvkkZUrNfxbWlqmdi4LFy2SI446WpYsO0LD26zLJ+BPq4SUlFgZvCKUwl26n84Os8ZhXPR3xCJ4KublCfZS27dt098/99nP9MgRjB8r61ItpbZuj26XxlhiKcPLf9KyawQSUJhd85HNvckIKHxoxQrNLyFUEm+8UXIDASDypp60sTkCX/jCF2ThwoVywQUXjM0DSHrd7wiMBVBIPWAvJQfT5UCFA0MQEQ8LA8LSQWB8ANRihpfXAAKnTq1S8+WBNECWA0HK0zW3NCsIZAwhA2EpCdGSJ4gHID+j4gWFaUm4ggLNP6ysmCKbN26SO/9yh6x8+GFp3rtXd58PI7hwkRxxNEBwmZaoY12rX5wvE4onyISSiVIcgCDrKBBFENO0V9lBQLCPD8eKkrq0rETuvuMOueP//T+ZM3u2/Pq3v5GJMWsdP3bC54SIvQQd6wOUqUeMojpp2TkCCSjMznnJxl5lBBSuX79ej11LOTU0al4OADFu+MrbOJYGJCTz6eWfsnHQkj71HIE777xTbr31Vvn617+eDM04HIFsBIWak6eegeYduB8bWFIS2cUAtnbvrlUBB0wgwC0OGgE2iEGwUplSWSHVVQO3SYFRdBBIreK6PfURCPM+4UvoIWJjBgnTWqUPxB4AwbKyErVo2bhhg9x5xx2ycsWKqE4ygG/BokVyJEBw6TIpUvCFGjhXCgoLlMWkhjDMoKt/ubc2722WBixx2toCQ2iG0xZWLtT77GHz5sncObPk09deKzf/4WaZOnWq3PLHW/XTG4rjmt01sjNWdYQ+I6IBMKtRdtKyegQSUJjV05NVncsoKEw/cm7m5OwAEnnweOOmRYiHMHP55PJ+E7azajTHWWfecv5bZPWzzwZLDUum139FfFLWqlC++KUvqifZ5ZdfLt/61rdkxowZ42wUksPJFlDo1UBcLRwP8SqwKi1VgERJN0LABgIbVMXbIyewIF8NomECKyunaHg2XTjR36zDusWBIAwcY0TOoPr5dXdbKFjTBLvNz09rDFvIuKAgTxk+hCzY1Kxfv07uvetuWbnyYdnb1GSMIEBwoQFB/ARh87q6u9RHELGJikXKMIUuihi6fe0dmv/Y1NSoeZHk+xEqViPq3Fy1quG4582dLQsOP1zHi3bDDTfIdZ//gm7ntzf9TpYuXarfcyw7dqZVHSmZqMKRpOrI2LovJKBwbM3XaPZ2VEFh/MB5qwYcAhKxNIg3bvQ44xNqJscmaYMfARLTH3zgAVmx4mF54IH75fof/EAWL17c74Ze/9rXyXPPPdfvMn+6/TaZMmWKbNiwQU455ZRel73rrrs033DJkiWD73iyxqiPwGiBQuxiAHf829tkJtDxRl4fYI7cPkAY6lcAGswc5dZoBoYKtMoIINB8AicNOp+Z7VqeYqPUNzYqM0nI2sCXqYWp+qEgMPxj/4BBKozEX6bKSkrk+efXy/1/vU9WPbJSmU4ahtQLFi5U+5ijjj5GQZpawrCBbqsJTC4hYJJ7IvuxvMC2iC1FsOJspDKCBQVqWTO9ulrmz58nM6ZN61FC7s+3/1muuPxy3f/3r79eznvNeXpcGGUDqr0RIkZ00p+/4qifqEkH+hyBBBQmJ8dARyBrQGG8w9wIDSDW6xt5j/yg/HwFiISZ8bxKvPF6n2rqoj704EOyYsUKeXjFiv3A3ee+8Hm56KKLDniekH9k9VndN62tx+9HHnmkPpD6K3N30onLVS05c+ZMOfeV58pZZ50lp59xhirSk5b9I5ApUEhYF/DnQDAePWCUXECRk5OrwKehCXCWOh9ZRnPrCinBVqxsFmCG/EC3lxnoaJPvZ2xgo31qSblmZeLYJ6wfoViEISQLulE1bB73K4CqVy/JzcvVcnE1u3bJLTf/QZ547DHdjrfFwVD6mGOPk6LiImX2aOQgot4F0MIK8kLMce+lxrGaZjcrUGZ//s8FKiiVOWbA4GGHze9Rei8+Bqe94lTZsWOH/Os1/yqvff3r9aXcx50UHkLESdWRgZ412btcAgqzd26yrWdZCQrjg6R5iLydBxYxnodouUCEmY1FTOxubOS+8fVvyDe/8Y0e51p5ebmceOKJsvyk5XICn8uXD9u5iGKxL1AIs/LhD31IAWp63tcZZ5whZ59zjpxz7jly+OGHD1t/kg0N7wiMFChkuwYAmxUMtrSmKohwBIA/DJoBOjBu2KZELyjt7QrElIFTs2irGIJNDGAIIDjYvGQ3suacRVXrIBCw2tHeof2AibOwtRlVk0+HrUu3UOkjANeCfAV05PI9/dST8tSTT8q6tWt7pMgsDIbSxx9/gpRNKhVCvx3ufZhDqblCmVw2SY8HoQoCEQAgY+BMoFYXgWHMzVWWkbJ2AEcA4ayZM7XkHN/1155//gW5++671coGEMuYITABDMKqJm18jEACCsfHPGbiKLIeFKYPAg8RB4jpIIM3agszEx46dFmo3//+9/K9735Plp94opxw4gly4vLlMn/+/BE7n/oDhb5TwnuwlvfcfY/cc/fdsnHjxqg/06dPlwceenDE+pds+OBGYLhAIYbPcSYwzpYBtHhwAUpysGrp6tKwLCXjWA8w6L57gEAMmieFUKqDwMHkBTIi7A8GEMYRIQrsOsx4cwCBngOoJd5ycxQM4v8HUDWxiIFDcvXoNxht29bNsnHDi/LQgw/I9pde6jHw+AiSI3jCics1D5f9cw+jpjC5hvqSW1oiZZMmSce+fRoW5rqBtSQvkU/WUTYQ70FAXLCe4X7H/Y98P5TA/dUTZpuab9kAC9qofWSOWZcqJb2pjg/uDErWHu0RSEDhaM/A2Nn/mAOF8aEl4Rv/L/cWi/+NG2ZVVaUKVnhzHixrMHamcPR7OhBQmN7LTZs2yV1/+YuCRPKoPv1vnx79A0l60OsIDBUUwurHcwL5mQa44m/tHZ2Sn4e5sQEurFXa2zsUAAJc8vNNkIHCVnPjioujUDCCiaH4nBL65X5BFRHYwJbmFmUo1bgZxq+7S4Uq6kCYAzw1n0IHkWoonStSkF8oOTnd6uv33Jq1snb1annh+fU92EBXDZMfCBDkhRW2j/tWFzmIgM28PCkuKpTi4gnKNLZ3tsu+NgPAPMjNuxCBCaxpniqM2S5iE3IFyS0EDBPiBdT1dZ9jG9iC7a6tjYAgx8T6KIg1TF1S0qcvYXJpjO0RSEDh2J6/TPZ+TIPC+EBxU1cGcU+9hpvjeYgsBzAk1MzDhM+xChLvveceDblmUxsKKMym/id96X8EBgoKYffiTCAsFIwaQA/hByFYve7ItwvVP2C/yI+DK+M7zRsssE/AD3nDgBVYsKGIzOgToomamjrZs2ePikVcjWyl5Axw5ecXiJAnaKSd5gQ6MGO53Nw8ZQgZC0Dgc2vXyJrVz0r9nj09Bo++Hr5goRx5zDFy/PHHS5mGf9s0PEzJOmdDtcpIIWbTVvGDPhnbGAOCebZP6hoTTvbwLr/zPetPq66WqsrKXnOrzS6nUU25yc/2eyLjSq4l1Viod0xjbGAb3dImuSbG1wgkoHB8zedIHs24AYXpg4QPIp6IPAR61je1N39AIswDtgyEn/oLt4zkBAx027fcfIt85StfkS2bN8vvb/6DHH300QNddcSXywQoxEeNZP33X/YBVTsnLXMj0BcoBHSoMpiUjoZGZe1hwgB/Cvba201sEXLVTJhB7p3l5cUBIEfD7y4KUXuZQaaAsE+YPwAQfoEeQYhqCXeacbSybvkWpvbqIQaYcgRRCKFaB2/kC27dskmtmQCD27Zu6fHCCcCaM3eelpg78uij5LDDDlewBiOpoV9yH6XbwuI5xkCyDscP6HQg6HmC7B/WjmXUdLvU2Dv+7i+y3LemT6tWYMc20hth+Zq6OqmrrdN5oLEceddUY8GfMH29BBRm7noajT0loHA0Rn1s7nPcgsL4dGi5qaYmq3/a1CQklKc3QjD+QBpqaGokToH77rtPvvTFL+lDiUblkOu+eJ0cf8IJI7G7IW0zE6DwmKOOjqyKLrnkErn8yiu0HmvSRn4E4qAQuxJqAmP/Ur+nQdr2tSnwcB9AV9y6ChaA47YssHGEhL1RfaMkiEK49mDDBtqoEQwARIChQrQGq1GsdjTtZhbtLCXbZL+YPWPvAih01oxQMayglnoDX+XkSF1NrV5va9cQEn5e2tLK5E2trpbDFy6SpcuWybJly6SkrEzyc3OlrX2fsp4wowBB9mPgj32YaMbAoQE5B8gKRDVvMVcZycmTy2RKeYUu65VDWJ5cPyxlsNZJbxx3bV2tsoLxXGstkzdligLI/qIjCSgc6Jk3NpdLQOHYnLfR6PUhAQrTB5aHFAAR77GmvU3qyxU3wrWHCEavVhUBJhFmsbe38pGatKefflqu+8J1suKhh3QXmEJ/5KMfkTeff/5I7XLI280EKNy2bZt87atfk5t+97uon1jqXPHBK5Oay0Oeuf5XROAB+7dz1261FCIXLt0mxsqrFaiVCvl/6hnY2aFCiLhdlBrSEwYO9jADVQdzXWpptgAA+RlmUq1o2rFJMhEKjB7l68yaxYQhADz642DI8hZzJI+QreIylstTMEkoGIXwuueek9qamh4DM7GkRA5bsEDrDB997LFSVVmluX0KOkP4Wxk5N6sGW1rpEGUNPQphIhoENd3SgaE0INWSF3VsZs6YJuyrsaFRj9kbCuTp1dP2KwXKfayurk6BoHsdsg4vuIBA1MOwjH4PecWpp/Y54QkoHKGLKEs2m4DCLJmIMdCNQxIUps8LDwuAIQDRgOLeHhUQWN7roarSsbRUc5xGwiNxT12dfOqTn5LbbrtNu1lRUSGXX3GFvPd9783a0ykToNAP/qWXXpLvfOvbcuONN0bj8da3vlUuu/xymTtvbtaOUTZ3jAcGJsykWcC4EX5taLS0C1fZUpbNPQBhrIoKixXsgL1QCac3DwU7COR6OVDT0myhNi9sPj+rOre728BfDASiCCYMTTjYS8apyXMIlQIGAV8whABU1Ql3dWnt4M6Odlm3br2sWb1a1j+3VrZu6RkSzssjJDxH2cAlS5fK4QsW2PWen69MIGNC7WItXxfC4QYxRdXJAEG3x+JlEuQHYKXL7cGA20HytGnVMmPadGlta9XcR7bpjWor1VVTo7w/3Ud3t84RdZWZJ3+Z5V6ELyOsYLyOPIznhRdcqHN58y03y5FHHdXrNCSg8EBn59j+ewIKx/b8ZbL3CSjsY7R5IKXYxL0akoo3buo8HHnD97zE4RKvnHPW2bJ792659P3vl/dd+r6sryKQSVDoc/Dyyy/L97/3PfnZ//xMv7ryg1fKRz760UxeO2NyXxp2VeBlINBLx8EConqNAzyATXGRlTPMzctRCxhAUPq1wEAMNhQM49gTALZGgIntmR+hAcGODivvpiIMQtVBsGEA0EKvhGY9TxHmEiaQCiOAR5bZseNleeqJJ2Tdc2tlwwsvSGuMiWM7VVOnyuELF8rCRYs1LEyIFpaNfQJWAZ/7NFRupePYvkcOCvJT4hhV8BbmK3PZtq9dWmPeiyzPvWLatGkye+ZM3UZNTa2Gv52BZbxRAwPu4vcTLdtXW6fMIKI6b5haV06pUECY/pK6edNmOf/Nb1aWF5bwxz/5cZ9CkgQUjsnLecCdTkDhgIfqkF8wI6Dwlj/+SWt0YqBMkvNYbJHRruYlWq3T9Ia9g4ebufkPVbzyxBNPyNy5c8eMoGI0QKGPPfu+4Qc/kCuuvFLPr6TZCACqMF3G7JhP/UdJto4OY9zazBqF3wFc5Puh+gVQqTnSxpIAACAASURBVAq1sEjz4kwsAShqj2rsDjYU7KyfegDyr7klsHup2WI/+/YZ46i1ekPpOkLYmDd7zh/hXrWNCXl5XGNe75jvLZcQo+sWeerpp2Tts6vl+fXr9gsJT5g4MQoJL126TKqnTdPjRgGtfWm3fQLsHISqUliVybmSX2Bm0dzPqK6Uk5snbYFpjZfjg3WsKJ8s1VOrZfr0al0Hj8Bdu2t6COAqKsplamVVD5aP+QE0snz8foPQBCAIcOzrHlNTUyPnv/l8FaYdd9xx8rNf/Lxf/8EEFI7vO0cCCsf3/A7n0WUEFP7i/26M3npJPFeD6fLJekMdiRDscA5QX9viYeosC4xiPAfI14FhcRYRRpGb+XhsowkKx+N4DvSYAC8AJsQe+tnWJjCBhFxdSEEIFYCoTCD+eF1dUbk4QCAgi/OS0Gt3J8xaioXyfgDAAEsIe0if6CsUDIhKB4Dpyn/fpqb3sc+ubqtT3N2tAIz129oAr6iELR/QawmbdUy+5vfiXcj3BiYRd3TKhufXq0Bk/bp1shWVcIxRYzuz58yRBQsXycIlS2Te/HlSOrFECouKFIBy/QJ82S/96eokGBzsaYIYpbCwSCZPKlM/QKqQYC5dV2tMnwttWAWGEZsYRCHV1VP1HodJ9m71RkzVE2bcyfsD3Hm4GRYQ1XBNXa2mtHjj7wBHlj1QKJ6cy7e8+XxZt26dLF26VG781S+1TF5/LQGFA73qxuZyCSgcm/M2Gr3OCCi88Ve/1qoEAEIeMA4E+cSHDICIXcJwhV9HYyC56Fy44mAxvR8cHw8L8pywV0EZOJaP2Y8vAYUjc8YBelzc4aAv/rtV3OjZPP8OcEEOHayb2pvk5+sn35P35uFYrsd0AVV6KJhsOcBdnIkFiDnr5wwg3/XWYB0BcTRCr2rg3LbPqodo3mBbxA769QDbh20M/YYJ1Lq/XV3GcGq5tzYFfjU1u2XlQyvkxQ29h4QXLFqkApFFS5boSyjHhuIYJpGxJBwdlc5UqxwDq1o6Li9f92uVPqbpfQvT65rdNdLcQq6jj3+OMnwYSM+aMUOrldAArCi1d9fURkyf5v4pK1gZpYUwZ/irAgSx0fI8QeaFPgMElY3sxX4mfbzZ5zve9nZ59NFHtYrRb2/63YAY9AQUjsw1nC1bTUBhtsxE9vcjI6DwN7+7Kbrx8kbNw8mNYeNDxNtsRWARhxp6zaYhd5DIJ0CRC/ORlY/I0mVLozd3wknkJqplRH6ehpcGW65rtI95LIDCH/3wR7J27Vq5+hNXS1VV1WgPWbR/DVGmsX3+e18gy1cGtGDjElUI2UdouE2vL7Nd6VYARrjTQSDXVRxcHCgUDGBC2IDnHyFmWEiAXJwZSw0mebYTjMkroF/kH3aoWphScoA/gKCLR1jPQKDlC5IXSH4eyl6uCfqsYfCWVmVACYU+99xz8sL6dbJp40ZpDhVSfP+Ef1EJwwYecdSRUl09TUUfjAVgiW1oeBlxirpUW16gvqgSEqZ+cFGhlsmkbjD3IsDfjp07VdTBvJichH7D3E1W82iAYPyara9vkF01u4VPb4BLVMtTKlK5f2wTMKhq6lg6Ckyg2shM6d9GpreT+MorrpDbb7tdZs+eLb/69a9k2vTpAzrXE1A4oGEaswsloHDMTl3GO54RUEgYgwcL+TF8xhVz2FjwAsxNMW4LQ7gVBpEE6rEGknqbRYQRH/nwR4Tybq847VR536XvVyuM3hoPMTXXDmWseNhlc6m+sQAKl59woibpE9r7wGWXyQcu+0DGwvmWF5cK8Zqow37vTbkbPyc493lRoN8AFlg31rFQa7OGJR2oqBiivV3dVhz4OSjybfamCuaBwfXXo48IUqgBHEQW8ZxCtgWA8vOSc5MwLLl3gL89dfVS39igQhEDgW3aJ3g1ytqZOMTyAukPx1UyEQN5y+dDVME6q599Rja8sEE2bXxR9jY1ybatW3tcLqw7e+5cVQcvPeJIOXzB4QruuKHAknJM9J99WZ1iA6FeMo5lAaAcB4zc1KmVUphfoC9w2PA0t+B76OxnjopuqqqmyPRp07W+cBxcsxx5gjCDLsTRyiFTKpQVJFTMOKu6e099jwoj9Itj0TxBli0qGvKD4IvXfVF+99vfym9++xuZM3fgavwEFA55yMfEigkoHBPTlBWdzAgo/P3Nt2gCO2//3PCwXyBMEs/Do44pD0DCRnHPLUaJh46GmMvLNZQ01trKlSvlissuV1BCPuWn//3f5E1vepMeBizB3uZmU4OqMKDFbC56afYgLo6qsTAWPNBGOy9zLIBClJif++xn5c4779SR5YH5X1/+LznppJMO+nTSMC+gKvj4Wag3levXW5jXdwpAUrAH6EsDf3wP8CDPrrGpUQEgVjEmqDAVMCCQmKeaRQfxQ/x88FAw5wrAg3WjUHQApprT10fzPD7y7kh90BeVIMgAPJEjhyqW65n+cA7DDvKiBxkH++f9cUNrQsKodAGsgDVy8lAHr352tbz4wguyedMmeXn79v3EKIwR1UNgAxctXixz583T2sEAQK0cgkuNGABkTtySxth3GNI8Td3gGuI7rZoCI5mTo+Xg6urrlcX0cLLbUE2tInw8XUO48cY+MPHevbumh8k0KTGMFfcs+rWnvkG3T41lYxutcU8sryiXisnlmqs5XK2hoSEKYQ90mwkoHOhIjc3lElA4NudtNHqdEVBITmF6c9NbHmrciM3N3/6RzI2fWPu+9v3qGAMqAYfccA+UcD0aA5q+z+u//32tSEIjt+kHN/xA5s2b12/XXDmq1iFBQdqbkCV6uBQWKljmYc0Dz3/O1PGPBVDoYwFAv+pjH5ctW7boVxddfLFc88lrDmj7Exdr8GA3yxQDf3G1aW9jrmHJXgAfIKe3NAm1Q2q06jteq1frB4eyaYQ+8d4rVOawMJaXmiOFBfl67WgIWRW8HQpY+2ckjQWLwGn4mfOIFzXWB2h0dHUZyxXqi8MEagm5rk5lAhUEBl9AcvKiGsc5OQGIFSlYxBAbMci6dc8pE7hl8yZpqK9PG7ocqSJHb84cmTt3nsybP1+mz5yhTKACvuBTiELaQKCVqSPyoOHnCeTrWjk7Ir4ch7Ku1BCmzJx0K5DlhQxW0rwOAWqFglk0YeHpqkje/yWU+5Wzgh5GB+DB8hH2xbpGQ+4NhMxbexwX88X9C0UywDhbWgIKs2UmRqYfCSgcmXEdj1vNCChcvXq13nwJd6Go4zPutcXAWq1QwmmdoSaq1UE124V8DSmRo+OqSr2BFxZI+WQDiLz1Z1PjGD/+sY9pfg/tta97rfzXl7/cry3EgfrvHnM8aJxZ5IGdXo2F7cDKADoMIAIUDTCORMH7sQQKfYwB6v/9k59IQWGhVou59tPXai4arJnX7o0++2HS4sC8L7bvQGKiOAikZi/zSz8cCLIPCx0XRipVY8Esd9DCmMYW9tVgJIudkVTQFwOBhT3Ly/EyUlu7R5kzGC4ADt+xDcATLKXtjzw8Uy9btQ4LK3tY2IQtHfLStm2yZs1a2fD887Jx44v6e0ea7+eECRNl5uxZMmv2HJkzb67Mn3+YspJqQdPVFZ3jBgb53+oJA2YBgGVlJbqs5lKioA5A0MeDXMWubky6g0dja0tUWo6QPGFe/AOnVvZu8wJ7DyOK1Qv3Mr/GYA8RySnjSb31xsYe9yjP2UR8wrLZGulIQOGB7r5j++8JKBzb85fJ3mcEFP7u939QoKf5O8XF+hDh5g3LYOFTvMuaQ4kqu3GT4E0eEwndgEJuvOTx8HbNGz5J2vFkdx5ALANAJHwzEKXeSA00YeK3XnChvPDCC7qLq66+SvPYRqoRXlSg2GrMIoCxP5ECYXyfB1STB8u4Zgso9LJjcTBnHnsdpjKFbVPbEavVu3PHTrnjjjv0Qf+uf3yXhvb7aoAKmDnP8Ys+A1gb6PkGgPeqOYReXcDgfoDOeAG28hTkoNa3T/YBEOJaitcQ9j6zHODRWL+ezJ8aOvfSOF9qa+qkrn6Pgho8ODl36Kd7/jFeAKoJRcVazs6Bn1buyDPWje+o9tG0t1k2bHhBXlhvAHDLpk37eQRy7eMLOHPWbLWJIS+QesIOcAPGVRWwdFMYrltyhPzDkMeoYhYTonh9YRewcYj01/KQu6U1sLptoSyevkzCJk7ADqZS7yn9OR9wf6oNIWJ/IWVsuYZgQ/k7YxhvzI/6F06apKzjaKd3DOS+k4DCgYzS2F0mAYVjd+4y3fOMgMLewsccKDdLBycARmciSJjnZrsHhiKUu/K8LLVpmDxJlXw8AHmAwTJGthIkkwcvxKqqylFjEN920cWqdv32d74jp51+WqbnVQF2FH4OilE3L+6tM/G5gFHU8mQDDG+NJChMB3M9QV57ZCnC9/3l7u1/zAYyADPksFHOzG1b/HuAIHl6fD9Q0Je+H/oPCAR4KvOmuXcIRQhZkv/WpXpWTZ0IoA9GEGBh//J72BYBCgEl+wE/bF8K8vs8z9RDsKVFgV/dnoYAAJuilwcHgISCuzq79JgRjxQUEobO1dgwQIr+0k8YfS2Lt6dBXggM4OZNG2Xblq3qMxhvpWVlMmv2bJk5e7bMnj1HQ8JaJSUof9Wjj2PHt1BLkRgLqcbUUQ6tgVGAMiCRe4QLbEhBQeRCfmGXAlgLL/uLpoeOOZ+nVlVFHql9DZaLQcgX9BdPQDLjzliQLhCPWLAdTOtJe4ER1NJ2Y6wloHCMTdggu5uAwkEO2CG8eEZA4Zo1ayw3LvxTiwkNke1fM9XBIg89NdXNEb3Bk2SPLQbhGW9xBSQPRLXgIJE7x9R83rC68Rt2psI31OgFSBCazKbm4ACw3dLGPLSpElYFC/00WCFsRgALccDCzwANKjYA0g/UCMOZojUweBGTN7SwbXx/MGUK7AKQU3++kF+X/r2bBR+ov4P9Oww3JsV40/Gg5eWG3DtXwMK4EWYFwMDecY5bbiHgs0Dz4Mwaxdi+KORbaMzfQPpNSgHXWFNzs/YBkAObDBvptYwN/HVGIVSAkzOQyr51dQfBk11Tza0tauWyY8cOtYPBHmbr5s2ye9fOHukL9G/ajBkKAvk3e85c88mLAUBYTpg//AIt8K2XrKU7qNK+WMP6CkxDaFtZYPqPVyH+grCZKJo7O3U7PPSc4YQJ5HxlXdhAZewmT+pX1QtwV9FMXV0EBNmespcBsMdfDDhOXk5122VlGfUbfWzVY7LsiGU6VsPVElA4XCOZndtJQGF2zks29iojoPCJJ540JoTE75ighBt9pLp1wKjqxd4BiuUq5SvjsbepOWJbPIepuIjQdJHe1AGdan0h3cpIcBNXEFlcrOXjCOvw80Aestk4cSPRJxdNAAK0FJrWnqViBMDRjH49yR/QYJUmjJHkAcxD2kKe5ovH+DPnZu0WjIGVDcsdcPcj42VYszCHKYBnggoHgZkI02koOpR+I8cTAAij1NhAVRssTACAnHWhIkYYE8bHX3QAd/j5aTk5gF8kQjHgd6AcRB889qP1gwObDjhH3AAoZN5ckZvKA7Rc08JCAKgpmzs7OR4Ti1id307NAzT/xDbZtmWLbN2yWbZu2aIsYHPz3h5zV15RoXmADgJnzpqlQhde5gB+HmomFMx/diZgTWO5iLBqjAEgzhlQUw6bpQzXsR5LMJpmq5xbNPrN1pQJLDARCUANkFZWWqbG032dE73Zw/Adx8yxsx79ic8FTKNtf5LO32g0TKnf9c5L1IbnlltvGbYuJKBw2IYyKzeUgMKsnJas7FRGQGFf4WNGJKU6Jocq2FfkiN6YI0Yp5IKR4O5ms25+jb0NN3JYQk+4d/BHSIcHjHuweZ6dsyI8pMgNgkXEPJr8upEQYmRy5rn4YVNgUFI/W2UL/b3TQpYOFPpe3pbR8GYw+uU4AA2+roYcCVM3N0tePkyt1Z7tr2leHOXKCgqUKVO7EBVAFEpxoeWsuTdlf+HQ4R5TqwlsQCqu9NXfOzpkzdq1Mq16WlCrcs5RWq29B/ijT5xTnF+8cFAKjWMBpAAIXS2sYUjUuYNozrQ7y47YAdYchb7328PRzLHC0u5uycuB6SIkKwr2TC1sc+r/mE9Kq+3cuVNqdu3S62n7S9vkhfXre/SQ45oxa5bmAWINM3f+fE0zYD7ZlplAgwaD4AV2UK9xrGDMTskVzeSxqtH1xIm6Dy8biZjMXkh8fK3WsEYMuuz6j5TEhYUGAMtKFQRi69LfuBLyrt9TryAe9pQGiFd1toafLZ3F2UllA4NAJNNsYG+nxjNPPyMXX3SRhsWv/OCV8pGPfnQQZ1D/iyagcNiGMis3lIDCrJyWrOzUoEAhN86vfvWrcsMNN2hlgYE82BYtWiS3/um2KH/KH1z+OZhRIYyMWCAKPYYQpOVDpUCkMTUWknKmQj+1vmsXuesaHku36YiqGmBpgWp3YomUEMrqI0l/MH0f7mU9dKYAMAJ7/QOyofZBH/a5eZHnnIJ3NwHOzVVfSUQaroZVHz3vV0fImwvfoToFxKTnZPXXNw8B8/CHieyrWT9jLGVujubHAXo6Og2w6nmiVS069NPNmT0/jW27ByB5f4AwUgFQnvKSgZAJAGz5cKboLSktVa+5ysoKmTq1SkGFWrKkNQfY/hmBMhV1UMLNvA4jljbY3vBSY7mUKcAKaFI/y0BIsi1V3nZZSJiXJELVHL8RdMa+7amrU4ENABD2bdvWLRoG7o2dNzHILBOEzJ2joWDXN6v4A7AWvjH2zlg82DVlRgmNa8UeM4cGAAIGAfuAWqxpamrr1LcUcEYf6DNAVg2ou7u0ioqyiMFSBuAHAORcYD56G+f4sLPdPfV71EYHex+aibKsPrQzuH6NA3JNJFJ2UE4BQ73W+lrv+eefV/Ea4O3Ct14oX7juumHdRQIKh3U4s25jCSjMuinJ2g4NGBRiTXHppZfqw/+uu+4aFChcn8Y4+GikAKI9sPr75yAjWiZUKVBA1NEprSHEqTVZg/1NK3lHMSNoBQ2AmZDf5ApLZ8uU7aBz4e9eGcJz0zS8VWwhpV07d8mcObMHHOrL1BlgoCiwrvFwfV6KiTVDYa/sYOxsFPbtZZ0DiSyGIjQBnEXMXMR2AYhMHeyCkr7Ao7Oh9hmYUP00ltTPl97seuJz4ecAZKgxoDCh6n4Xkt0AvY1SW1Nr/drXJnPmzpGjjz5KykpKzTw5hNF50eDFJWLhAmvr++sJSmMANYDV6LoA1Ol3qePy5DsPS2uFjvDyY5+GDu14u7U+766dO6N/u3fvkt07d/YQZMXHgTAwAHDWLBOE8DNCE2Xmw3Z75tcZA2k1gg0EWk5gccSOAgYBgVw/ADL19qupUXspwBqhazdq93NM/RwDAGSbbMNBILZTAwmtA6IBOQ4EFWiHf5z3XMMwt2wrYgODUngg28/Utez7wXj9wgsuEK6z817zGvn+9d8f9i4koHDYhzSrNpiAwqyajqzuzIBBISfVn//8ZznttNNk+fLlgwKFD61YESXVZ7pkHb5vu2t2KytBMjmWJBpCJW8oLzeyGDFPtU61sGjTPCbCVx1RMn4Uts7N0VAbJbdmzZ4ly5Yuk4klE0NuVE/LkpHMV+RR3TNH05i80WhDAYXeT88f81A08xIxeJo20KHMjj/YvYqHgh/FRQGEhZxF+z71ndX9NQCjYE+BmtW/1Vq4QW3L/iMAGULcAD7PA+xo3yf333e/bNmyWbtOXd3zXnOeGhbHX3JSTGTvoM/Bj51Phjthv2EuwXkWsjdgB8BUT8CgprWorKl0vb+M/c4dO1TwwYsKnztefrnP06B4wgS1f5k6tVqqp1XL1GnTZMaMmVKETVR4GfLwr1q+5ORZfmAoSQdLGgdu5Oa6kbxXLGLnhIERbSC02b5jRyS2MdANe2kWO9jcwCi6MISfAX8WEi4dcM4vL4Jc6zt37YrqjHPesD/LVbR845RvoCmFD9aOaaSvNxjdN7/pH2T79u163/35//5iRCIXCSgc6Zkc3e0noHB0x38s7X3AoNAPCgXwYEFhPKcw3frEbtYoMA+sXD3YgeUBoR6HDfX6qf5rgc3hgUg+kStBASbka6mHYkuz4HNGyGnz5s1q6Asgo/wVgBCWzVkHQK96zOEnF68PqxYvE1UNOR6aW5gAYngQ84BVti2wdPbwD2yXM3fxvzkL1kdJvwONEf54btmSUkOj3s0zoNfRqYBSlbhBxGTCmSCgCTVtOR99fRUqlFnokPJnqGA9DEt//MXo5z/7hRqtA7DOPutsOf2sM5HIa+hTswoD4Isz4Vr1I8eAKWHgjnaYUmNGHRgDDi20bGUOzZ4FJrxDdu3erazf7l27wudO9f/rK4ezpKTUwF/4Ryi4aupUPS7PrYjn5/Iz4g/3ROSFxr0YPU2kunqqAjXLB5zYo9oH+Y1btm6Nqp3ErVws99JyA7nWWd/U7CYucRBI3t5AX6QYM3IDd+zYKbtra1Vs45VlUmyg3Vc85MwnYpGBpL0c6PzLxN8Bauf/w5tl48aNsnjxYvnN7347YlVQElCYiRkdvX0koHD0xn6s7XlYQeEjjzyy3/G/7W1vk+9df4OGiZTdiLEEqYeSJaN77hAVBoqKCSOZLYfniWnCubIXIW9MrSJ65pClKjwceCqortLQuH85KvrFgwsWBDsb2CLCX5++9loh2bu8Yoq8/ZJ3SHV1tbS2tAVDZGNAPBkedsXz8Mi98qYmws68qCEy+VJF6p/moSt9QOebZQnWHCrMwMvtIFvfIVfzptM5cuYsHobtEZ4NTE+sLzAyzNOBwsx9db9HvmIIc7ta3D4tzOdKZMAE44ydDvlo9mlKVc+Nc1CvjC/l2Do7bRshZIhi2eZ4koL1koklyiSlytmhug6l7MKne2GyvwceuF/Wr1uvDNvSpcvkyKOODPYuRv8puFNkZ7V428ilJDcwGGerGESvBRsVxg5QSJjXwF+K+aurre0zB7Ns0qQe4M8YwGkKWFNCkpRAyw2fo/SBXGPLOccZEx9jrwuMOpjSeVxXAEGOnRfD+kbq+TYpEwi77s1D5BwX1yagTMsvhqon7KtMwRk5gSUDZr0YT8LOWP3U1NYoE2lehdZ4AUOkxFyS4oK5NerjgXptHuSlNSKrY4L/zre/Q19sbvzlL6WyauReKMkL7qvs4ogcXLLRjI4A1w/uBGoPlbRxOwLDEYkdVlB4zTXX7DfYv/71r+Wb3/mu5a3pA9+EApykan2hFhgWauur8aBSJk4f6LBwPQ19e1vPK0A4SIw+I2BpPmkeMjOQYQno6RUK6OOdd/w/ef75F9Qc94orr5DDFhwePfxd3Wxm0W36sPck/3YNS5o3HUwaD39/WB/ozHRTE+sj63r+X0+hh+cIUufVEu/j5c7MCsaBx1CBW3pfTWxi/eF4ALApJTlz7bWsQ+5izIoo3Zqov3FwaxTUvoSQeUCq8jfN4zKyisE2h/BrjpmYEwJ2VbuBS6pwEBLNUQCsAodYabvechBNyGNMX3Qe5+XKnro9svrZZ2X5KScbQ9nB9gxIck7HBSUgRA3/aj3ids3v83Dvrl3GACIC6W3/7HdyebmCPUDf1GnVUllZJVXBG1LXCYpfz8H0Fy43xeZc17JwqvYuiux9uLbilYZcIaym8G1typTzMAH8Mf5uA+PXsKmOc62ecDB4Znv+EsNYI94AgAPSBira8msRRr++0WoIt7a09lB7cwOEXdQqRqWlUlw8oV8D7wNdb9n4d3JZm/Y2ydy5c0e0e6q+dveHEd1TsvHRGgHuOwO9/karj8l+D24EKioqDm4DPKK6D5SJn7aLoYSPr//hj/Sh4Ynqxny5otDYMNgIwmUoIpX1wWqmFSBgvmEGpFI5ZPyizEYAiF4WjAefhfGG3tgXwIM+8FCidnNrS4teUEuXLdOHkHuqpTN4rGvefqkwZfoQ8ztjoOpNrDZsIkwdmy64ieXIDfSI0sOCEUAIIpuIdaNsWDE+cYU9AB3zBGvL33rLW0wPv/HgKq8oP6iwHA8lB9c29m0aso8rxGH8bHwI7XdIJ6HVoCRmbIIdos1/t0TA1MD0/nWBfV7in4BZFd0AJvk51PS1/TJH5JnaC01bm4WjUwKTlH2P1gzG+mRPnYJHQsAAm+fWrtHv+2pTKis1X3Ha9OlSVT1VKqumatgXY+u4QlqrdgSLlkh1zctDqIVsoVkYQPMCRPGLWpfwLaygVRIydhewh8qaNAl8Dq3qih2bAWI7Xq5he7kINY8x2CYfUH0JbXzZNiBQyyeWlPRrGO1jwNzDAgI8Gxqb1PuRuefaj187gEB8AqdOYYyqlWlM2vCMQBI+Hp5xzNatJOHjbJ2Z7OtXRkDhv17778pdaeg3vI3ykKOElpYS4wEMi5OXL0UTiqV0YolMKjPrCR5iPNB4SMHCUUKLTzW1DXlh6cNqnnBFUlZSot5wPLTZPg+1yKqD8J7bdoQHfm9K12s+8a+q+jvs8MPlH95yvvbRnoz2AXDi4coDUOuhmmtvcKyz5ehvS0uzVpXQknydqUouDlV4uOZrCD149oUa0YyNMlmAn3bz0uNh7fV9GZeotm8ITaoAw4UXpsbo4UsXHy/mo7fQdF/f93YK8wDXnFD3pwsLqW41Gg5TsTrI6KHEDWDYVa6ReCTyRzR2VYEQDFwAfQYEjQZVYBRjgRW4xvrjSnJjjHMlL98An557IaRsTHaujjUAtB1fP8Y8vKh4iL2ttUUtauqpF6yl6xoU6DU2NlhYu7lFdu7c0e/VDtCD+QP8wf5VVVdLZVVVxLymxDKpzThbnLLeMTY2lf9nQL5yyhSZgDk2KluslULo1sseutcheYBxo2vOo4jFDqpjhpcXA/ZBKBaw6WkO/Azg1CokEydEf+/vwBkfDLcZ15raWhWjIBLxfE8HgcxlQWGB5hsi5pk2daqmcyRtZEYgAYUjM67ZstUEFGbLTGR/PzICCmErNJeobJKyFdRCLVWfAlkXrAAAIABJREFUsUlSOgmlIYXjJ8lELD5CiC7FblkVFE9K9yoImi+EOjEvzwx5Ow0w6UM8JO/3Nvxsh1CWl4iCQYqECgDVkFfl61Ki79PXflpuuOEHgm0HYcuG+gbZE0rupQNJwln4nFF3ua+EdvpLPiNebXubYUia+wyfu+kvD19/wNP3/pLlHSiSc6WAUv0c8eQzI2arWAKbyd9CBY404KjgwFBXaPEaHSlajj8DCgHfKTBqqlnYMUK07NtBIMDOAI8D11R4O6V+jXaZVh0kuOJpaNhSCXqKTIzlS4WuPYQdTNHxIOxh7E3pNAOAJvog/7BDQ7m1dbVSXwfwq7fPhgZpqN+jv5MbeKBGTh9Ufnl5hbKokysqtJIOTOC0adMN4MZMpHtsL6QZ6DWQawIQgFhPUUyRlE+eJOXkz3E+h5cIzt84+GtpbVEWUJnrYM4deQIq02iAWvMgu7tDzWOrEAIo40XKKnzkSOWUylCGzkDgQPJcORcRhOi53gQT2Ghh6DDmfty+P87xKRXlUjWlUkFgEu460Jk2PH9PQOHwjGO2biUBhdk6M9nXr0GDwsEeAubVKEEH0rC7iEAjBrUIPahUQKH5sslSRokpbCRKAY8WeuWBxnpxEYLmt+WR50SeG4pPwl8GUlQFqSXY+vhnvFOkjuxZ6xd20ypxOBgh5GX/mjUEFg938RC3XCpTPQJk+3qQGhPaag/0FstrhEHpq2ELUjzBQoNxsOjLO+Aw8YspYzXXMcaOOlMaB22e3+nWIZGCFhsfFU34PwM1gMwmVWNbTp2XSItAZQQso8TGyNvOc/5cfet5pqxi82ugCLCIGId8NwAQYwkIjZdMZM6UhXSvQbW2sTk3W5s2DY/W7NotO3bukJ07d6l6t66uVsO7hHkBfMxllITZx+Crt93kcplUPlk/ETZMrijXJG5AYEXlFD33FEZ3i4qUmCdCu6YsNhDmKmNj/lLhajufgwF0EeKJEikttfrdnvPn6Q1akYMUi3CNsS9NYVAz6BQQtJzIUGs4sK7GMNq57Oc04FPHeYK9ONFvrhcYxb6S1FM5tVR6aQ2iH1h9K7cX5VmGPFD3/dQXtJKJMqW8QkPBXPuZqk0+kPvRobRMAgrH92wnoHB8z+9wHl1GQOHnv/RlaWpoUBNgQm0krvNZW1trJrO1ddLQUK8h4YE2VJcog2EZFTxOmqwMJKBRfy+bpGEnZ9Q8j86tYnhApwCOV90woDOY5iFHE11gZGw5WKbiJRfSSvkp1IThIkQeSrsVFuKfZjVo002z3cfNBRSW5E8NWBNGxFm5eK6li3JS9YEPLMoZyPEa02gAKyo/GMKNnsAcB9qwW16OzIQME2TCxGIpLiwytrK9Xf0gm5nzUCLN+6GCiJCvpqkAhQW6T4Ahx47YwVXFDjrw5oO9JYxr4pEOeXHDBq3Zi4CDUG9/uXzxMeDcAgBxTsHyTZo0Wc8rZfzKK4S/ewUP5tvC1vaSonMdAB8AG3aMfjEeADsAl54zMSU07B7nAspZQC9WOAUFdl4YwDORjVYx6UWQZbWBrRoILxTkXHrzc8MZcVe0K/OOOXQI/ToA5AUjvQHuAMukZMAKR4pvxB8x1lRLBUZ9pWpNp6WH5Lt9UIGyf7DpBnQHrj4eyDk6Fpd59plnZM2atfKWC94yqt1PQOGoDv+I7zwBhSM+xONmBxkBhV/66tctDIh5cMgT83QvD1HyOw8Vy81qjPK1qFVa31CvbJTmb6FEbGkZ0ASg2AQYujpTbSpKS7V+64yZM6LQqDNShLDIxSLcTY4fDy61EfZQqtqMAByN5dFSX5YtGdLXes+hc/BpSs2U4MFBFA9owAIPaS/pdqAD9Jq8nltoIfQUGIgDNPWG1O1bFQfy/9x+wsP1gAYTFBDqtXBzFFbd1x6xstp/BbF2zAA/+kIeG2NWRPg9CA/Iwdvb0iLNzXuleS9+j+RUtkb5gSro0dzQNrPEURFHZ2R6vLepSdfRz1Clpnlvs54njL+aUXd3y0vbtvaZX5o+jhMmTFRwB0CbNHly9E+Zv8kGAgk/mwgoqI2D+TXgj79FCmYdMxOfMAZq6UNt6KA2BygyJwBWLD8QURFSPuLIIzQUC1gGNHldX4Bffy8lHoJnzJWFUzX2PjtHCQXn5kQVSyxnN8UCas5rLP/PxCeIV3q2nqyfAUBM35m3OGBk3B2cO6us+Y2anwkQtNA+TLn7A3LtHags3YHO+/H099tvu10+9tGPanQAD8Ljjz9+1A4vAYWjNvQZ2XECCjMyzONiJxkBhTff+sdIjav5bsHY2OrSmoI0ClvG8qw86V1Doa7+DLVd8W6DbSS5X/3SlIVsVDYSAMnPgJHhaLAoAB5TbhZr2Fa91wjdhvAtIMuYMUQuVtkEZkVV1qH8F9uAgYqzbhrSDkDZ0/cACSa+QYiTr/ldVp4PNtLYKFXUBmFEpJLFZiVW39eZRatTG8QaoRYwAMYFOGyLfoBOzMfOSwEqvxn893KD2htlbqosHn0HsPGJSps5aWps0pBpa0uzMkw89LATIb8NQK/2IrCEhGqHqSnoUbFPiRlPByYKVm9SCPEi7rCxMwWte0mmxCYAGZs7AFsE0vPyInETIWjYOAeBURlFr4IS1L+wm1qpQ1MNCmXN6mdlxYqHFQDDFp988kly4vLlveaGOqD3cn/Kju4LuZ8hyTMusmJ7yjaGtAYUup43y4sQ+X/xHFT1cwyhXOaOuTIGsPdcSbcFIrzLK01bCE07++4vOrxwmFG0KY/HskfgMJ2WfW7m29/6lnz9a/ayDEv4+S98YUAl/EaqXwkoHKmRzY7tJqAwO+ZhLPQiI6AwXvtY88Zc+NDDpzCIIbD6UDsKwoSWj5QCkgYiPXypD2avkoGYIQDGSEEpogwN4IOKB83NTdLSHB7qwfOOhzSsCyxOin0xFmagjORQJhrWxGopmwhn4aJF+uCOV9Dw7Zrpd6hvGxOEpIe/HWDHP+N1gOOiEbYdaUjCjmIcpn0TM1b2XwERL2/fPpRD7nMdAAQAukgZWjMs52e+8/Hxv8H0wYDxu4J0li8uttzSYLmjCncqykRACeFEQdg2gK9YJqoVjzGnjBchWFhIABLHCJCFuQM8e+UbrzXMsLi9Ep9eqxdwri8AlIwLKQPxg+ZcpG74mtWrFQygNn7DG96g9iod7e1CrW6z2LFzOb0ZE5dvSv38fLV9oQKLVxdRD8XcXAV8VjsaIGlbcaY13d8xfR+we4TsGU8vCelK//TQMueth4Exo4aNTlr/I8A96yMf+rD86U9/0nm89tpPyzsveeeoD1sCCkd9Cka0AwkoHNHhHVcbzwgofODBB/Xhy4OZ0KKGSPPMxHogjQeosokxMOlsWwTkAHUqJghMFEBP7Vvao4dsutWJM3Rsgwdc/EHuOX7+QEVxqgnzYbuEPTXPK3yvSf1qsGzLATLjQDOqjjGIvMmBjM1oLWNWQeYxqUIFPtVOx0oFGriznx3wKcALoWuAHADPm9f1Tf1uQiCvwKFhyZAHpxZAEycGYFgYlLemiNV9FxZGYgvmAxEQwh2EQAB9zhFn+5S1DkbTkTI6NqiE12FsAVvO/mL14secHg6lnxqaLyxQ1K35kyht9bxo13Dsyy+/LM+vf17Pz6qqKlmwcEFsHKhmY8Ip85C0ijcOYAkR03hJ0By+YEnUn/l7+jlijLaZjZvohZQIEyNxXgOE441ta4pAZWWPcHCiDB7c1VdTUyPve8975amnnlJRzQ9+eIOccsopg9vICC2dgMIRGtgs2WwCCrNkIsZANzICCuO1j+NjokBCQWIq9KW5UAWpxPSB2F70Nc4ellZjXsJkjY0KDNSnraVFf16zdq0+8Mglm45VSKiFrIAxVQpEd9GzTogpn91bT8Os6g1oilM30E4BUX2U63ZghQxAmngAwKDfKSvqdh2EDC3HzHPbvMRf5PcYBA7u/egAKifHlKzqx8dnyPXab71QIUW/RyjD8lScUeCB6jeEWUNpQcCRtTjHaKDCByiyFgzCGq+z66NnfpVmEWPKbguPE5In9DipbJJMrZqiZecMuGDFkvK3dJW2haBNAEHVjVZC06HaCUAJoKd5lp56EGNY4/OqOZXh2L1PAFqv0evAx70MVcATxkH9+gjZB5aPOVULGF4Y2tr2yw/U2tCBAeS4tm7ZLKjzSSlgBM0DEIWySHdIqRjMPcSvJRV3hGuKviJ41jrUwR7Iq4X0lb+oOaiwqVrjeEL0ApeUyBrMbPRcFmur977nvZpfOnfeXPnRj38shx9++NA3OMxrJqBwmAc0yzaXgMIsm5As7k5GQOHd99xrytnYv3Q2or8xilvARA8+t4WJgcjBjDPK54sufKts27ZNzjz7bPmP//gPY0rw8AtmxYQQLUcvZXUS/a6iDivxBTuUAmYpgULcY04T2EJJMGw7lFEkxKdjAlvVIR0hn9IMmg1oxS1u+B0Q48rksEkTucQMq8OvvQyH9Vf9AMl9C0t0EpoOYNiAggHb9PCy7VtlNdqHKBeyq0uBFd+zjlsFeW6cVwnRcdIqIflRpZT0TrqFTqTiDukBKkppsxKCPexuAkZ1F8X08YpX+9DwcjCsttB9kQJS6k8X6nlUEGp0W9WU4EGu3oWNe5vs/AVoBvsXf4FwkBl3cmQstKxeXr7kB78/25eFsvvzmYyPSaTcjSl44/6MbsXEsfGS4fmablANUO4L/Kn9jOfKBpNrC9f3FKAw7lwLCSgczB2m57IPP/ywXPKOd8oxxx4rP/zRD9XGKJtaAgqzaTaGvy8JKBz+MR2vW8wIKIznFPpAqsedAqJgLxJyoMxg19ScnjM40MGPMyXugcbD35s+oPPzlDG8+K0XyfPPPy9nn3OO/PgnP+5zF16uzsLCKc81Kw1moNH89SwMuY8Qd+g/qtQ4cwZooA8pAXIKZAEUtF6vGhWbjYyxUqHaS26eAjm3O1ETZg2rdymgbCcPrQPPOuujCnfcNBp7nOAvGA+hW9/2zyyMrFVgCykMIinPwBSoNP9A61N3qDzjfnfWfw+7Wj8Dc8enhvUBVx1aNcRy6GK2QA6KXfUdZmc/wBcqmTgDCsvpbKoJSizP0NXlCvICeNZxCyXz+NmAZvpY9H3meQUVAK8rxq1cI1VFLGweB6Raezj0Kf4C4T/rfAeGPO652VcPsLlxk2oYU37uq1l9YyqbpCqcePh/INdWAgoHMkoHXmblypVy8sknH3jBUVgiAYWjMOgZ3GUCCjM42GN8VxkBhX/8020pdis8yM3WJIRgYwyUWZ4YG2VMkyiTZqbEBiDUlDj62axYeLBHwoh4ebUeP4uGGG+9+RbZvn27HL5ggbz1wgujKVRT68jY2hg1Z+V6lsQDiHVJR1eneeLtQ7mZ8pEzoYexTQAiZbec9eulQkgUUoV9U+ASAydOV8VOtIgJDADH/9TD6zBmfRMBQWXZzE6nKxXxNWYP0BLUzF4/16bCQrcupjA7m2Ida8aLdVB6A4wAovHqKR6+H4z3I3yjs8hR2Dyorr1snh1PKJnngoxQBcTL6vkQuoG01k8Jx9wX+DPLGauU4nl9gDxl+IoLZUKRqc7JZ4RN8zzUCPz1Ii4Z6P1BBS36YtTRo3b3li1bFWD251Po+1CRSPCE5FOB4IRU+HegfUlfLgGFQx25sbNeAgrHzlwNpacJKBzKqB2a62QEFP70578Ifn49kY2FL+OZevbrYL6PYZ8UEOsyZspKiTlLhq9auyZ5o0DGw3DJkiXB6y4wRSHhHtChFUACoDMBgtFMMUzXy+8B5IYcPAe48VMLoBmZTQcA6MDFfA81KB2FcE0HoEHZFKunrJb97n+zXEarluF1jz2sHAfLEWMV8vQ8/zEecu7JJjqQVFi7H7HoYNcZLzvWtOXSrW7IKdTOub9jGNmwmnruhZeD1Ngxbl09wvRm0WPWMtY89zBVBzmeXxdV7kAQE/6pCCYIL4ZTOKHijDSj78j8O4A/V9HDjvfVfv6zn2mo8ZWvepXavNBcTIPa1xTYqfrGI3EbS0DhSIxqdm0zAYXZNR/D3ZsEFA73iI7f7WUMFPYAVXGAlfZzBLviLNggflZGL1bKzTwODeSh+qS8GQn0s2bPCjlwTh+lAT5TkAR7agNlhmPMuDnFZtp3bgIdBzq9/ex5dh7ejJtMG+LKsUoomGR3Avq6pNPBacyrUUGvh0AVNMbzAAO6Ciyjg6bIODuMuXoXxmB5CvDuH0ZV0Bk33o5dEyydOh4X4LjJtdc4DibgyvK5ujVWyUUxnbHDhFkt/ExOXhprh7IXFXJQPsPWKcArKoxKHTrLdzAipfglz8tEbx5+MHuIlay+tNWWVtPvfkBef7cSVecHIQufW7ZskWs/+UkV1DCK77v0fXLppZdm/G6UgMKMD3nGd5iAwowPeUZ3mIDCjA73mN5ZRkDhj37yU+NxInRirE4UGfXQn33dg1W0ag/GiPXw5Yv97n9zQ+Z0hiw+Qy+99JL6wvHQdXWuChACEImDEBScroZWJiyEk1Of4Zi0kznSJZS1I1xs6mNnGvl0+xDAnNuIOJCIcuoIg0cxTgNmxnaG/LcAAqOQaACjmgMYA092DOTSpYyao/BpyJ1jTHuKMKxMnzF+xrgpQMEYOdR71vw8wushtO/hYYzEyR/UXFDNqTRBhgJyoyJFA+ihqg0/q9ULOZ5e8i2IMsjRMzBtIDx1DPbdWGk+fm6/5IKRVK6oqZj1X4FZ3vTWEEJ9+tpr5Z6779E/L168WD5/3RcyWv0iAYUDO+uonZ1tApKB9Vy03Kia9MdysAe6brJc9o9AAgqzf46ypYcZAYW9WdKY96An+4fKJg5+4p+q/A2K2AGMWlSaLOTHaSWQkORvpsaW8A8AOliMEYHRWJUQLdcWBAypnw0gHqi5ZUmU9xfAsIknHCiZj52yY1phxVS0cQW01tV15WuPn73mrv29v+Yg1oU2+hlsczSPsn1ftDo+gFiXpIM29aakOkgwodY8NzWdLgpG3VbNJl6FJf67GZXb3/erghPOkd78+VzZ6/1x6yDPYx3spwtVIlFIsNThHPIcRLeqYW445uFulET7zGc+o5Ym9Ofit71Nrv7E1ep3N9ItAYX9jzDXynVfuE5u/sMf5LY/365+jmOtJaBwrM3Y4PqbgMLBjdehvHRGQOEfb7tdmbIeOVbtVr/WhRUuhI3n1+nEhNAxylIPKeqDOGYDw9/cay4YBxpLFwQJ7h/Y47sQku1EdOHmxQrCUvmFllvo27GwdJyx5OcegCOIZyLLGPrvIdFITWyl6wBusIkKHAk5dlp1FlXQKkNmOXeAN8LdWkO2pERKSksUEB4Ma0a/I7CH6XZMVe3AbyDiEFhUBBfYoEyZMkXBn5f4o4/q45e0YRsBPBm/+pWvyn//5Ce6TcDHHX+5c8TZqQQU9j2FW7dulQ9ecaU8/fTTCtCv/8H18opTTx22Oc/UhhJQmKmRHp39JKBwdMZ9LO41I6CwL/Nqs+FwGxPziUv9TlitQAFU3NPNS7gpGxfzEDRWzlTIatSrCuVgdeKl8AL482UGwt71N6lmdmxGwSnTbVi4YMAdPgF3VLLANqS5uUX2Njer597+LUdKSgwAOhCEVRtsc5ufvlg+ct8O1ACnAD61WdHwcfhU2xX72YHprl27FKAM1HvvQPtO/t7/CFBj+uqPXyXz58+Xb33n2yM+XAko7H2Ib7rpJvn3T/+bltI85phj5Dvf+67MnDlzxOdjJHaQgMKRGNXs2WYCCrNnLrK9JxkBhX+97/7I7kQZvVyqNiCkCKHW/UCbKYbdNNoBnworIpHCwQ9tlFMYmMaIcQzhQQsz27+Ud1wKrPbGhCnwazEA6D/3BcLc3sQBICHY/hqspStWETns64PlOzDYzYksVbTkWShTFwd/g2H5ElB48OfiULbAgzwThtIJKOw5O7CCV33s47Ju3Tr9wwcuu0yuuvqqoUxh1qyTgMKsmYoR6UgCCkdkWMflRjMCCvtiCoc2ouaNp1UyNG8w9nNMMKKALiznIpLouyAqOZgQrJZbC+CvmdJmlM5rbe0zdxAAyL+JfFLTtrjQgK/6LprXYip/zv0YMaA2Y2r1r3NPvgMMHEyl++j1BviG03qFriSgcGhn8lhZKwGFqZn6+te+Lt/65jf1i2nTp8uX/utLcsYZZ4yVqeyznwkoHPNT2D+h0NUl1N6eOnXq+D7Q5OgOegQyBgodwFmZs5Af6NYjDvKUsesJ+FwY4grhAwG5VY+ukhtuuEG+/Z1vRzVqD3aUmgPrpzWUW6iz26q2I2p9o5VFgu0N5d4IKYewd15BnuSHY4qDv4Hk6/XWZ47dFaseZlemLy28e6AxOtjxSF8/AYXDPaLZtb0EFKbmg5zO737nO/L2d7xdrrr66sg7MrtmbPC9SUDh4MdsLK2RMIVjabZGt68ZAYW9lbkbicPGvuPv/+6NUldXJx/68Ifkn/75nwe0GxfBAPb2NjXL3pZmaW5uVn84/Olg69waJl7ZxMGf5RTmKxgcWF6d18V1NbCrWK08nNm0WN1cPl3ZOpiQ7oAOfJgWSkDhMA3kMG/mwQcelOu//325+l8/IUccccSQt56AwtTQcY9Y/exqOeHEE4Y8ntm4YgIKs3FWhq9PCSgcvrEc71vKGlDoymD1tnPVb1ADW6k4Uwb7z6YKdmPqbs3f+9QnPymoAefNmyefuvZatQZxtXD6NvfC+Cnr12Z5ep2UGOvsdb7j7B/1aV1I4oxn5LUXGFDYvN7AnS4X/o2nEysBhdk5m+9+1z/KX//6V+3c6aefLq9/w+vloosvHnRnE1A46CEbcyskoHDMTdmgOpyAwkEN1yG9cEZA4a1/ui2qKmKGzvEycm774lUuhjYft9x8i7z44ouq2r3o4osi/zbEKgg9UnY4np+X2p+LSbTGb1GRTNCascXqvTdxwkS1Wokzdw7uMh2mHdrIjPxaCSgc+TEeyh5gu394ww1yww9uUOabRk7Ru9/zbnnHO9854NBnAgqHMvpja50EFI6t+RpsbxNQONgRO3SXzwgoHKjQBDUw1TTUgJpqHG7arPVt9//ODZ1/f9NNcustt0ppaZn884f/RaqqqjTnD8+99n3tUR1dr8SBlyFsXmlJqZSVlf7/9s4EOIsii+OPK5CgRCUrWIgVlFhBASEgIoF4wMqykSMQ0CpD5JCAHJGlBJYopQRYhYIQLglyR45IEAjKuSwgQRKKIClwNZJoWeXFoXKUiazAsvUakw1nZr6vZ6a7v39XUR41X/d7vzfk+6Wnu4dCglkCr2wCQbNPAFJon5mbn+DlFPwO5TWr19CJEyfE0Hy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   ],
   "source": [
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=y_true, line_color=charcoal, line_dash=\"dash\")\n",
    ")\n",
    "\n",
    "for j in range(25):\n",
    "    fig.add_trace(\n",
    "        go.Scatter(x=x_full, y=fits[j], line_color=\"rgba(153, 157, 160, 0.5)\")\n",
    "    )\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=x_full, y=np.mean(fits, axis=0), line_color=charcoal)\n",
    ")\n",
    "\n",
    "\n",
    "fig.add_annotation(x=2.02, y=1.51, text=\"True g\")\n",
    "\n",
    "fig.add_annotation(x=9, y=4.0, text=\"One f\")\n",
    "\n",
    "fig.add_annotation(x=5.66, y=1.57, text=\"Average f\")\n",
    "\n",
    "fig.update_layout(height=250, width=400, showlegend=False)\n",
    "fig.show()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We can see that the 25 fitted quadratics vary with the data. This concept is called *model variation*. The average of the 25 quadratics is represented by the solid black line. The difference between the average quadratic and the true curve is called the *model bias*. "
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "When the signal, $ g $,  does not belong to the model space, $ \\cal{F} $, we have model bias. If the model space can approximate $g$ well, then the bias is small. For instance, a 10-degree polynomial can get pretty close to the $g$ used in our example.  On the other hand, we have seen earlier in this chapter that higher-degree polynomials can overfit the data and vary a lot trying to get close to the data. The more complex the model space, the greater the variability in the fitted model.  Underfitting with too simple a model can lead to high model bias (the difference between $g$ and $\\bar{f}$), and overfitting with too complex a model can result in high model variance (the fluctuations of $\\hat{f}$ around $\\bar{f}$). This notion is called the *bias–variance trade-off*. Model selection aims to balance these competing sources of a lack of fit."
   ]
  }
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